SOLVED EXAMPLE

158

PHYSICS FOR NEET & AIIMS

SOLVED EXAMPLE

Ex.1 A sonometer wire resonates with a given tuning

fork forming a standing wave with five antinodes

between the two bridges when a mass of 9 kg is

suspended from the wire . When this mass is

replaced by a mass ‘M’ kg, the wire resonates with

the same tuning fork forming three antinodes for

the same positions of the bridges. Find the value

of M.

(A) 25 (B) 20

(C) 15 (D) 10

Sol.

9g

f2

5

Mg

f2

3

9g Mg

f M 52 2

5 3

f M 5

Ex.2 A particle of mass 50 g participates in two simple

harmonic oscillations, simultaneously as given

by x1 = 10(cm) cos[80(s–1) t] and x

2 = 5(cm)

sin[(80(s–1) t + /6]. The amplitude of particle's

oscillations is given by ‘A’. Find the value of A2

(in cm2).

(A) 175 (B) 165

(C) 275 (D) 375

Sol. 2 2 2 2

1 2 1 2A A A 2A A cos 10 5 2 5 10 175

2 2 2 2 1A A A 2A A cos 10 5 2 5 10 175

2

A2 = 175

Ex.3 A steel wire of length 1 m and mass 0.1 kg andhaving a uniform cross-sectional area of 10–6 m2

is rigidly fixed at both ends. The temperature ofthe wire is lowered by 20°C. If the wire isvibrating in fundamental mode, find thefrequency (in Hz).(Y

steel = 2 × 1011 N/m2,

steel = 1.21

× 10–5/°C)

(A) 11 (B) 20

(C) 15 (D) 10

Sol.

TAY T YA T YA 48.4N

Y T YA T YA 48.4N

Y T YA T YA 48.4N ;

T 48.4v 22m / s

0.1

1

for fundamental note

2 2

2m f 11Hz2 2

v 222m f 11Hz

2 2

Ex.4 Two tuning forks A and B lying on opposite sidesof observer ‘O’ and of natural frequency 85 Hz movewith velocity 10 m/s relative to stationary observerO. Fork A moves away from the observer while thefork B moves towards him. A wind with a speed 10m/s is blowing in the direction of motion of fork A.Find the beat frequency measured by the observerin Hz. [Take speed of sound in air as 340 m/s]

(A) 5 (B) 6

(C) 7 (D) 8

Sol.

sound mediumobserver for source 'A' 0 0

sound medium source

v v 33f f f

v v v 34;

sound mediumobserver for source 'B' 0 0

sound medium source

v v 35f f f

v v v 34

Beat frequency =

1 2 0

35 33f f f 5

34

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159

Ex.5 A progressive wave on a string having linear mass

density is represented by

2y A sin x t

where y is in mm. Find the total energy (in J) pass-

ing through origin from t = 0 to t =

2.

[Take : = 3 × 10–2 kg/m; A = 1mm; = 100 rad/sec;

= 16 cm]

(A) 6 (B) 7

(C) 8 (D) 9

Sol. Total energy

2 21A

2 4

Ex.6 Figure shows a stretched string of length L and

pipes of length L, 2L, L/2 and L/2 in options (A), (B),

(C) and (D) respectively. The string's tension is

adjusted until the speed of waves on the string

equals the speed of sound waves in air. The

fundamental mode of oscillation is then set up on

the string. In which pipe will the sound produced by

the string cause resonance?

\\\\\\

\\\\

\\\\

\\\\\\

\\\\

\\\\

\\\\\\

\\\\

\\\\

\\\\\\

\\\\

\\\\

L

(A)

L

(B)

2L

(C)

L/2

(D)

L/2

Sol. (B)

Ex.7 A transverse wave, travelling along the positive

x-axis, given by y = Asin(kx –t) is superposed with

another wave travelling along the negative x-axis

given by y = –Asin(kx +t). The point x = 0 is

(A) a node

(B) an antinode

(C) neither a node nor an antinode

(D) a node or antinode depending on t.

Sol. At x =0, y1 = Asin (–t) and y

2 = –Asint;

1 2

y y 2A sin t (antinode)

Ex.8 If y1 = 5 (mm) sint is equation of oscillation of source

S1 and y

2 = 5 (mm) sin(t + /6) be that of S

2

and it takes 1 sec and ½ sec for the transverse waves

to reach point A from sources S1 and S

2 respectively

then the resulting amplitude at point A, is

S1 S2

A

(A) 5 2 3 mm (B) 5 3 mm

(C) 5 mm (D) 5 2 mm

Sol. Wave originating at t =0 from S1 reaches point A

at t = 1.

Wave originating at t =1

2 from S

2 reaches point AA

at t = 1.

So phase difference in these waves =

2 6; A =

2 2

1 2 1 2A A 2A A cos 5

Ex.9 String I and II have identical lengths and linear mass

densities, but string I is under greater tension than

string II. The accompanying figure shows four

different situations, A to D, in which standing wave

patterns exist on the two strings. In which situation

it is possible that strings I and II are oscillating at the

same resonant frequency?

String I String II

(A)

(B)

160


(C)

(D)

Sol. Since tension in I > tension in II

VI > V

II Thus, for same frequency,

I >

II

Ex.10 Which of the figures, shows the pressure difference

from regular atmospheric pressure for an organ pipe

of length L closed at one end, corresponds to the 1st

overtone for the pipe?

(A) (B)

(C) (D)

Sol. For pressure standing wave

Note

fundamental frequency

antinode

A

first overtone

NAN

Ex.11 A standing wave is created on a string of length 120

m and it is vibrating in 6th harmonic. Maximum

possible amplitude of any particle is 10 cm and

maximum possible velocity will be 10 cm/s. Choose

the correct statement.

(A) Angular wave number of two waves will be

20.

(B) Time period of any particle's SHM will be 4

sec.

(C) Any particle will have same kinetic energy as

potential energy.

(D) Amplitude of interfering waves are 10 cm each.

Sol.

6 120 40 k A v 1 T 2

2 20

6 120 40 k A v 1 T 2

2 20

6 120 40 k A v 1 T 2

2 20

max6 120 40 k A v 1 T 2 6 120 40 k A v 1 T 2 6 120 40 k A v 1 T 2

Ex.12 Two strings, A and B, of lengths 4L and L

respectively and same mass M each, are tied

together to form a knot 'O' and stretched under the

same tension. A transverse wave pulse is sent along

the composite string from the side A, as shown to

the right. Which of the following diagrams correctly

shows the reflected and transmitted wave pulses

near the knot 'O'?

OA B

(A) OA

B

(B) OA B

(C) OA

B

(D)

Sol. The wave suffers a phase difference of when

reflected by denser medium.

Ex.13 Three progressive waves A, B and C are shown in

figure.

With respect to wave A

B A C

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161

(A) The wave C lags behind in phase by /2 and B

leads by /2.

(B) The wave C leads in phase by and B lags

behind by

(C) The wave C leads in phase by /2 and B lags

behind by /2.

(D) The wave C lags behind in phase by and B

leads by .

Ex.14 A man generates a symmetrical pulse in a string by

moving his hand up and down. At t = 0 the point

in his hand moves downward. The pulse travels

with speed of 3 m/s on the string & his hands

passes 6 times in each second from the mean

position. Then the point on the string at a distance

3m will reach its upper extreme first time at time t =

(A) 1.25 sec. (B) 1 sec

(C)12

13 sec (D) none

Sol. Frequency of wave 6 1

3 T s2 3

6 1

3 T s2 3

; 1λ = vT = 3 = 1m

3

Total time taken = 3 3T

1.25 sec3 4

Ex.15 Two mechanical waves, y1 = 2 sin 2 (50 t 2x) &

y2= 4 sin 2 (ax + 100 t) propagate in a medium with

same speed.

(A) The ratio of their intensities is 1: 16

(B) The ratio of their intensities is 1: 4

(C) The value of 'a' is 4 units

(D) The value of 'a' is 2 units

Sol. 2 21I v A

2 and velocity =

k

Ex.16 Following are equations of four waves :

(i) y1 = a sin

xt (ii) y

2 = a cos

xt

(iii) z1 = a sin

xt (iv) z

2 = a cos

xt

Which of the following statements is/are correct?

(A) On superposition of waves (i) and (iii), a

travelling wave having amplitude a2 will be

formed.

(B) Superposition of waves (ii) and (iii) is not

possible.

(C) On superposition of waves (i) and (ii), a

transverse stationary wave having maximum

amplitude a2 will be formed.

(D) On superposition of waves (iii) and (iv), a

transverse stationary wave will be formed.

Sol. Superposition of waves (i) & (iii) will give

travelling wave having amplitude of 2a

{waves are along x-axis but par tic le

displacements are along y & z-axis respectively}

1 2

x xz z a sin t sin t

v v 2

Ex.17 Three simple harmonic waves, identical in

frequency n and amplitude A moving in the same

direction are superimposed in air in such a way, that

the first, second and the third wave have the phase

angles

,2

and () respectively at a given

point P in the superposition.

Then as the waves progress, the superposition will

result in

(A) a periodic, non-simple harmonic wave of

amplitude 3A

(B) a stationary simple harmonic wave of

amplitude 3A

(C) a simple harmonic progressive wave of

amplitude A

(D) the velocity of the superposed resultant wave

will be the same as the velocity of each wave

Sol. Since the first wave and the third wave moving in

the same direction have the phase angles and

(+), they superpose with opposite phase at every

point of the vibrating medium and thus cancel out

each other, in displacement, velocity and

acceleration. They, in effect, destroy each other out.

Hence we are left with only the second wave which

progresses as a simple harmonic wave of amplitude

A. The velocity of this wave is the same as if it were

moving alone.

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Ex.18 A progressive wave having amplitude 5 m and

wavelength 3 m. If the maximum average velocity of

particle in half time period is 5 m/s and wave is

moving in the positive x-direction then find which

may be the correct equation(s) of the wave? [where

x in meter]

(A)

2 2

5 sin t x5 3

(B)

t 2 t 2

4 sin x 3 cos x2 3 2 3

(C)

t 2

5 sin x2 3

(D)

2 2 2 2

3 cos t x 4 sin t x5 3 5 3

Sol. 3m

2 2k

3

Maximum displacement in half time period = 2a = 10

m

So maximum average velocity = 10 2 2

5 T 4 sT

2

10 2 2

5 T 4 s

10 2 2

5 T 4 sT 4 2

Ex.19 Two identical waves A and B are produced from the

origin at different instants tA and t

B along the

positive x-axis, as shown in the figure. If the speed

of wave is 5m/s then

(A) the wavelength of the waves is 1m

(B) the amplitude of the waves is 10 mm

(C) the wave A leads B by 0.0167 s

(D) the wave B leads A by 1.67 s

Sol. Wavelength of the waves = 1m; Amplitude of the

waves = 10 mm

Ex.20 A standing wave of time period T is set up in a

string clamped between two rigid supports. At

t = 0 antinode is at its maximum displacement 2A.

(A) The energy density of a node is equal to energy

density of an antinode for the first time at

t = T/4.

(B) The energy density of node and antinode

becomes equal after T/2 second.

(C) The displacement of the particle at antinode

at T

t8

is 2A

(D) The displacement of the particle at node is

zero

Sol. Equation of SHM of particle who is at antinode

is y=2Asin

2

tT

at time t =T

8

y= 2Asin

4= 2A; Displacement of particle at

note is always zero.

Ex.21 You are given four tuning forks, the lowest

frequency of the forks is 300 Hz. By striking two

tuning forks at a time any of 1, 2, 3, 5, 7 & 8 Hz beat

frequencies are heard. The possible frequencies of

the other three forks are-

(A) 301,302 & 307 (B) 300,304 & 307

(C) 301, 303 & 308 (D) 305, 307 & 308

Sol.

3 7

1 2 5

300 301 303 308

8

7 3

5 2 1

300 305 307 308

8

Ex.22 Two notes A and B, sounded together, produce 2

beats per sec. Notes B and C sounded together

produce 3 beats per sec. The notes A and C

separately produce the same number of beats with

a standard tuning fork of 456 Hz. The possible

frequency of the note B is

(A) 453.5 Hz (B) 455.5 Hz

(C) 456.5 Hz (D) 458.5 Hz

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163

Sol. Let frequency of note B be n then according to

question

nA = n–2 or n +2

nC = n–3 or n +3

As A & C produce same number of beats with T.F.

of frequency 456 Hz so

(n–2) – 456 = 456 – (n–3) n = 458.5 Hz

(n+3) – 456 = 456 – (n–2) n = 455.5 Hz

(n+2) – 456 = 456 – (n–3) n = 456.5 Hz

(n+3) – 456 = 456 – (n+2) n = 453.5 Hz

Ex.23 Consider a large plane diaphragm ‘S’ emitting sound

and a detector ‘O’. The diagram shows plane

wavefronts for the sound wave travelling in air

towards right when source, observer and medium

are at rest. AA' and BB' are fixed imaginary planes.

Column-I describes about the motion of source,

observer or medium and column-II describes

various effects. Match them correctly.

Column I Column II

(A) Source starts moving (P) Distance between any two

towards right wavefronts will increase.

(B) Air starts moving (Q) Distance between any two

towards right wavefronts will decrease.

(C) Observer and source (R) The time needed by sound to

both move towards left move from plane AA' to BB'

with same speed. will increase.

(D) Source and medium (S) The time needed by sound to

(air) both move towards move from plane AA' to BB'

right with same speed. will decrease.

(T) Frequency received by

observer increases.

Sol. Velocity of sound in a medium is always given in the

reference frame of medium.

Ex.24 A tuning fork P of unknown frequency gives 7 beats

in 2 seconds with another tuning fork Q. When Q is

moved towards a wall with a speed of 5 m/s, it gives

5 beats per second for an observer located left to it.

On filing, P gives 6 beats per second with Q. The

frequency (in Hz) of P is given by (80 × (

I, 0 9) then find the value of + . Assume

speed of sound = 332 m/s.

Sol. Let f1 and f

2 be the frequencies of tuning forks P and

Q,

Then | f1–f

2 | = 7/2

Apparent frequency for O corresponding to signal

directly coming from Q = f2 q

v

v v

Apparent frequency of the echo = f2 q

v

v v

f2 = f

2

q

2 2

q

2v v

v v

Since, f2 = 5 (given) f

2 = 163.5 Hz. Now, f

1 = 163.5

3.5 = 167 or 160 Hz, when P is filed, its frequency will

increase, since it is given that filed P gives greater

number of beats with Q. It implies that f1 must be

167 Hz.

Ex.25 Two vibrating tuning forks produce progressive

waves given by y1= 4 sin(500t) and y

2= 2 sin(506t).

These tuning forks are held near the ear of a person.

The person will hear beats/s with intensity ratio

between maxima and minima equal to . Find the

value of

Sol. y1 = 4sin(500 t) ; y

2 = 2 sin(506 t)

Number of beats 1 2n n 506 500

2 2

= 3 beat/sec.

164


As I1 (16) and I

2 4

2

1 2max

2min

1 2

I II

I 4 2 2I I

2 24 2 6

9I 4 2 2

Ex.26 A 1000 m long rod of density 10.0 × 104 kg/m3 and

having young's modulus Y = 1011 Pa, is clamped at

one end. It is hammered at the other free end as

shown in the figure. The longitudinal pulse goes to

right end, gets reflected and again returns to the left

end. How much time (in sec) the pulse take to go

back to initial point?

Sol. Velocity of longitudinal

113 1

4

Y 10u 10 ms

10 10

Required time

3

2 2 10002 s

v 10

Ex.27 Find the number of maxima attend on circular

perimeter as shown in the figure. Assume radius of

circle >>>.

Sol. S2S1

1.7�

0

��

��

0

1.7� 1.7�

1 in each quadrant, 1 top point, 1 bottom point

WAVES

165

SINGLE OBJECTIVE NEET LEVELExercise # 11. The speed of sound in oxygen (O

2) at a certain

temperature is 460 ms–1. The speed of sound inhelium (He) at the same temperature will be (assumeboth gases to be ideal)

(A) 500 ms–1 (B) 650 ms–1

(C) 330 ms–1 (D) 1420 ms–1

2. A wavelength 0.60 cm is produced in air and it travelsat a speed of 330 ms–1 . It will be an

(A) Audible wave (B) Infrasonic wave

(C) Ultrasonic wave (D) None of the above

3. The speed of sound in air is 332 m/s. The speed ofsound in air in units of km per hour will be

(A) 1.1952 km/h (B) 11.952 km/h

(C) 119.52 km/h (D) 1195.2 km/h

4. The speed of sound in a gas of density at apressure P is –

(A)

2p

(B)

3/2p

(C) P

(D)

P

(E)

2

P

5. The intensity of sound increases at night due to

(A) Increase in density of air

(B) Decreases in density of air

(C) Low temperature

(D) None of these

6. Sound waves travel at 350 m/s through a warm airand at 3500 m/s through brass. The wavelength of a700 Hz acoustic wave ass it enters brass from warmair

(A) Decreases by a factor 20

(B) Decreases by a factor 10

(C) Increases by a factor 20

(D) Increases by a factor 10

7. When a sound wave of frequency 300 Hz passesthrough a medium the maximum displacement of aparticle of the medium is 0.1 cm. The maximumvelocity of the particle is equal to

(A) 60 cm/sec (B) 30 cm/sec(C) 30 cm/sec (D) 60 cm/sec

8. Speed of sound in mercury at a certain temperature

is 1450 m/s. Given the density of mercury as 13.6 ×

103 kg/m3, the bulk modulus for mercury is

(A) 2.86 × 1010 N/m3 (B) 3.86 × 1010 N/m3

(C) 4.86 × 1010 N/m3 (D) 5.86 × 1010 N/m3

9. Consider the following

I. Waves created on the surfaces of a water pond

by a vibrating sources.

II. Wave created by an oscillating electric field in

air.

III. Sound waves travelling under water.

Which of these can be polarized

(A) I and II (B) II only

(C) II and III (D) I, II and III

10. If the frequency of human heart beat is 1.25 Hz, the

number of heart beats in 1 minute is

(A) 80 (B) 65

(C) 90 (D) 75

(E) 120

11. A progressive wave y = Asin(kx – t) is reflected by

a rigid wall at x = 0. Then the reflected wave can br

represented by

(A) y = Asin(kx + t) (B) y = Acos(kx + t)

(C) y = –Asin(kx – t) (D) y = –Asin(kx + t)

(E) y = acos (kx – t)

12. Two waves represented by the following equations

are travelling in the same medium

1y 5sin 2 (75t 0.25x) ,

y2 = 10 sin 2(150 t – 0.50x)

(A) 1 : 2 (B) 1 : 4

(C) 1 : 8 (D) 1 : 16

13. A sound wave y = A0 sin(t – kx) is reflected from a

rigid wall with 64% of its amplitude. The equation

of the reflected wave is

(A) 0

64y A sin( t kx)

100

(B) 0

64y A sin( t kx)

100

(C) 0

64y A sin( t kx)

100

(D) 0

64y A cos( t kx)

100

166


14. The equation of a transverse wave is given by

y = 10 sin(0.01x – 2t)

where x and y are in cm and t is in second. Its

frequency is

(A) 10 sec–1 (B) 2 sec–1

(C) 1 sec–1 (D) 0.01 sec–1

15. A wave travelling along the x-axis is described by

the equation y(x, t) = 0.005 cos ( x – t). If the

wavelength and the time period of the wave are 0.08

m and 2.0 s, respectively, then and in appropriate

units are

(A) 0.08 2.0

,

(B) 0.04 1.0

,

(C) 12.50 ,2.0

(D) = 25.00

16. Which of the following equations represents a wave

travellign along y-axis

(A) y = Asin(kx – t) (B) x = A sin(ky – t)

(C) y = Asinkycost (D) y = Acoskysint

17. The function sin2(t) represents

(A) A periodic, but not simple harmonic motion with

a period 2/

(B) A periodic, but not simple harmonic motion with

a period /

(C) A simple harmonic motion with a period 2/

(D) A simple harmonic motion with a period /

18. Two waves are given by y1 = a sin (t – kx) and y

2 =

a cos (t – kx) The phase difference between the

two wave is

(A) /4 (B)

(C) /8 (D) /2

19. The wave function (in SI unit) for a light wave is

given as (x, t) = 103 sin (3 × 106 x – 9 × 1014 t) The

frequ ency of the wave is equal to

(A) 4.5 × 1014 Hz (B) 3.5 × 1014 Hz

(C) 3.0 × 1010 Hz (D) 2.5 × 1010 Hz

20. A wave travelling in positive X-direction with A =

0.2m has a velocity of 360 m/sec. if = 60m, then

correct expression for the wave is

(A) x

y 0.2sin 2 6t60

(B) x

y 0.2sin 6t60

(C) x

y 0.2sin 2 6t60

(D) x

y 0.2sin 6t60

21. Three sound waves of equal amplitudes have

frequencies (v – 1), v, (v + 1). They superpose to

give beats. The number of beats produced per

second will be

(A) 4 (B) 3

(C) 2 (D) 1

22. Two periodic waves of amplitude A1 and A

2 pass

through a region. If A1 > A

2, the difference in the

maximum and minimum resultant amplitude possible

is

(A) 2A1

(B) 2A2

(C) A1 + A

2(D) A

1 – A

2

23. If the phase difference between the two wave is 2

during superposition, then the resultant amplitude

is

(A) Maximum (B) Minimum

(C) Maximum or minimum (D) None of the above

24. Two waves are represented by y1 = 4sin 404 t and

y2 = 3 sin 400 t. Then

(A) Beat frequency is 4 Hz and the ratio of maximum

to minimum intensity is 49 : 1

(B) Beat frequency is 2 Hz and the ratio of maximum

to minimum intensity is 49 :

(C) Beat frequency is 2 Hz and the ratio of maximum


(D) Beat frequency is 4 Hz and the ratio of maximum


WAVES

167

25. If two waves of same frequency and same amplitude

respectively, on superimposition produced a

resulant disturbance ofthe same amplitude, the

waves differ in phase by

(A) (B) 2/3

(C) /2 (D) Zero

26. Two source of sond placed close to each other, are

emitting progressive waves given by y1 = 4 sin 60 t

and y2 = 5 sin 608 t. An observer located near these

two sources of sound will hear

(A) 4 beats per second with intensity ratio 25 : 16

between waxing and waning

(B) 8 beats per second with intensity ratio 25 : 16


(C) 8 beats per second with intensity ratio 81 : 1


(D) 4 beats per second with intensity ratio 81 : 1


27. Beats are the result of

(A) Diffraction

(B) Destructive interference

(C) Constructive and destructive interference

(D) Superposition of two waves of nearly equal

frequency

28. Two sources produce sound waves of equal

amplitudes and travelling alonng the same direction

producing 18 beats in 3 seconds. If one source has

a frequency of 341 Hz, the frequency of the other

source may be

(A) 329 or 353 Hz (B) 335 or 347 Hz

(C) 338 or 344 Hz (D) 332 or 350 Hz

29. Each of the two strings of length 51.6 cm and 49.1

cm are tensioned separately by 20 N force. Mass

per unit length of both the strings is same and equal

to 1 g/m. When both the strings vibrate

simultaneously the number of beats is

(A) 5 (B) 7

(C) 8 (D) 3

30. Two tuning forks of frequencies n1 and n

2 produces

in beats per second. If n2 and n are known, n

1 may

be given by

(A) 2

2

nn

n (B) n

2n

(C) n2 ± n (D)

22

nn

n

31. The distance between the nearest node and antinodein a stationary wave is

(A) (B) /2

(C) /4 (D) 2

32. A string is stretched between fixed points separatedby 75.0 cm. It is observed to have resonantfrequencies of 420 Hz and There are no otherresonant frequencies between two. The lowestresonant frequency for this strin gis

(A) 205 Hz (B) 10.5 Hz

(C) 105 Hz (D) 155 Hz

33. The phase difference between the two particlessituated on both the sides of a node is

(A) 0° (B) 90°(C) 180° (D) 360°

34. In sonometer experiment, the bridges are separatedby a fixed distance. the wire which is slightly elastic,emits a tone of frequency ‘n’ when helf by tension‘T’. If the tension is increased to ‘4T', the toneemitted by the wire will be of frequency

(A) n

(B) 2n

(C) Slightly greater than 2n

(D) Slightly less than 2n

35. Consider the three waves z1, z

2 and z

3 as

z1 = A sin(kx – t), z

2 = A sin(kx + t)

and z3 = A sin(ky – t). Which of the following

represents a standing wave

(A) z1 + z

2(B) z

2 + z

3

(C) z3 + z

1(D) z

1 + z

2 + z

3

36. If we study the vibration of a pipe open at bothends, then the following statement is not true

(A) Pressure change will be maximum at both ends

(B) Open end will be antinode

(C) Odd harmonics of the fundamental frequencywill be generated

(D) All harmonic of the fundamental frequency willbe generated

37. The condition under which a microwave oven heatsup a food item containing water molecules mostefficiently is

(A) Infra-red waves produce heating in a microwaveoven

(B) The frequency of the microwaves must matchthe resonant frequency of the water molecules

(C) The frequency of the microwaves has no relationwith natural frequency of water molecules

(D) Microwaves are heat waves, so always produceheating

168


38. Standing waves are produced in a 10 m long

stretched string. If the string vibrates in 5 segments

and the wave velocity is 20 m/s, the frequency is

(A) 2 Hz (B) 4 Hz

(C) 5 Hz (D) 10 Hz

39. The velocity of waves in a string fixed at both ends

is 2 m/s. The string forms standing waves with nodes

50.0 cm apart. the frequency of vibrations of the

string in Hz is

(A) 40 (B) 30

(C) 20 (D) 10

40. A uniform wire of length L, diameter D and density

is stretched under a tension T. the correct relation

between its fundamental frequency ‘f’, the length L

and the diameter D is

(A) 1

fLD

(B) 1

fL D

(C) 2

1f

D (D) 2

1f

LD

41. A student is performing an experiment usinig a

resonance column and the tuning fork of frequency

244s–1. He is told that the air in the tube has been

replaced by another gas (assume that the column

remains filled with the gas). If the minimum height

at which resonance occurs is (0.350 ± 0.005)m, the

gas in the tube is

(Useful information) :

1/2 1/2 1/2 1/2167RT 640J mol ; 140RT 590J mole .

The molar masses M in grams are given in the

options. Take the value of 10

M for each gas as

given there)

(A) Neon (M = 20, 10 7

20 10 )

(B) Nitrogen (M = 28, 10 3

28 5 )

(C) Oxygen (M = 32, 10 9

32 16 )

(D) Argon (M = 36, 10 17

36 32 )

42. The number of possible natural oscillations of air

column in a pipe closed at one end of length 85 cm

whose frequencies lie below 1250 Hz are (velocity

of sound = 340 ms–1)

(A) 7 (B) 6

(C) 4 (D) 5

43. A closed pipe and an open pipe have their first

overtones indentical in frequency. Their lengths are

in the ratio

(A) 1 : 2 (B) 2 : 3

(C) 3 : 4 (D) 4 : 5

44. A pipe of length 85 cm is closed from one end. Find

the number of possible natural oscillations of air

column in the pipe whose frequencies lie below 1250

Hz. The velocity of sound in air is 340 m/s

(A) 12 (B) 8

(C) 6 (D) 4

45. An empty vessel is partically filled with water, then

the frequency of vibration of air column in the

vessel

(A) Remains same

(B) Decreases

(C) Increases

(D) First increases then decreases

46. Doppler shift in frequency does not depend upon

(A) The frequency of the wave produced

(B) The velocity of the source

(C) The velocity of the observer

(D) Distance from the source to the listener

47. A motor cycle starts from rest and accelerates along

a straight path at 2m/s2. At the string point of the

motor cycle there is a stationary electric siren. How

far has the motor cycle gone when the driver hears

the frequency of the siren at 94% of its value when

the motor cycle was at rest (Speed of sound = 330

ms–1)

(A) 49 m (B) 98 m

(C) 147 m (D) 196 m

48. A band playing music at a frequency f is moving

towards a wall at a speed vb. A motorist is following

the band with a speed vm. If v be the speed of the

sound, the expression for beat frequency heard by

motorist is

(A) m

b

v vf

v v

(B) m

b

v vf

v v

(C) b m

2 2

b

2v (v v )f

v v

(D)

m b

2 2

m

2v (v v )f

v v

WAVES

169

49. A source of sound S emitting waves of frequency

100 Hz and an observor O are located at some

distance fromeach other. The source is moving with

a speed of 19.4 ms–1 at an angle of 60° with the

source observer line as shown in the figure. The

observer is at rest. The apparent frequency

observed by the observer (velocity of sound in air

330 ms–1) is

(A) 103 hz

(B) 106 Hz

(C) 97 Hz60°

(D) 100 Hz

50. A train moving at a speed of 220 ms–1 towards a

stationary object, emits a sound of frequency 1000

Hz. Some of the sound reaching the object gets

reflected back to the train as echo. The frequency

of the echo as detected by the driver of the train is

(speed of sound in air is 330 ms–1)

(A) 3500 Hz (B) 4000 Hz

(C) 5000 Hz (D) 3000 Hz

51. Which of the following has high pitch in their sound

(A) Lion (B) Mosquito

(C) Man (D) Woman

52. A spherical source of power 4 and frequency 800

Hz is emitting sound waves. The intensity of waves

at a distance 200 m is

(A) 8 × 10–6 W/m2 (B) 2 × 10–4 W/m2

(C) 1 × 10–4 W/m2 (D) 4 W/m2

53. If the pressure amplitude in a sound wave is tripled,

then the intensity of sound is increased by a factor

of

(A) 9 (B) 3

(C) 6 (D) 3

54. A point source emits ound equally in all directions

in a non-absorbing medium. Two points P and Q are

distances of 2m and 3m respectively from the source.

The ratio of the intensities of the waves at P and Q

is

(A) 9 : 4 (B) 2 : 3

(C) 3 : 2 (D) 4 : 9

55. Intensity level of a sound of intensity I is 30 dB.

The ratio 0

I

Iis (Where I

0 is the threshold of hearing)

(A) 3000 (B) 1000

(C) 300 (D) 30

170


SINGLE OBJECTIVE AIIMS LEVELExercise # 21. A boat at anchor is rocked by waves whose crests

are 100m apart and velocity is 25m/s. The boat

bounces up once in every :–

(A) 2500 s (B) 75 s

(C) 4 s (D) 0·25 s

2. The waves produced by a motorboat sailing in

water are:–

(A) Transverse

(B) Longitudinal

(C) Longitudinal and transverse

(D) Stationary

3. A wave of frequency 500 Hz travels between X and

Y, a distance of 600 m in 2 sec. How many wavelength

are there in distance XY:–

(A) 1000 (B) 300

(C) 180 (D) 2000

4. Two wave are represented by equation y1 = a sin t

and y2 = a cos t the first wave:–

(A) leads the second by

(B) lags the second by

(C) leads the second by 2

(D) lags the second by 2

5. The distance between two consecutive crests in a

wave train produced in string is 5 m. If two complete

waves pass through any point per second, the

velocity of wave is:–

(A) 2.5 m/s (B) 5 m/s

(C) 10 m/s (D) 15 m/s

6. The displacement y of a particle executing

periodic motion is given by : y = 4cos2

1t

2sin

(1000t) .

This expression may be considered to be a result

of the superposition of ......... independent, simple

harmonic motions.

(A) two (B) three

(C) four (D) five

7. The displacement of particles in a string stretched

in the x–direction is represented by y. Among the

following expressions for y, those describing wave

motion are:–

(A) cos kx sint (B) k2x2 – 2t2

(C) cos2(kx + t) (D) cos(k2x2 – 2t2)

8. Two waves traveling in a medium in the x–directionare represented by y

1 = A sin(t – x) and

2y A cos x t4

, where y

1 and y

2 are

the displacements of the particles of the medium,t is time, and and are constants. The two waveshave different:–

(A) speeds

(B) directions of propagation

(C) wavelengths

(D) frequencies

9. A transverse wave is described by the equation

y = y0sin2(ƒt –

x). The maximum particle

velocity is equal to four times the wave velocityif:–

(A) = 0y

4(B) =

0y

2

(C) = y0

(D) = 2y0

10. Dependence of disturbances due to two waves ontime is shown in the figure. The ratio of theirintensities I

1 / I

2 will be:–

(A) 1 : 1 (B) 1 : 2

(C) 4 : 1 (D) 16 : 1

11. The equation of displacement of two waves are given asy

1 = 10 sin (3t + /3) and

2y 5 sin 3 t 3 cos3 t , then what is the

ratio of their amplitude:–

(A) 1 : 2 (B) 2 : 1

(C) 1 : 1 (D) None of these

12. A plane progressive wave is represented by theequation y = 0.25 cos (2t – x). The equation of awave is with double the amplitude and halffrequency but travelling in the opposite directionwill be:–

(A) y = 0.5 cos (t – x)

(B) y = 0.5 cos (t + x)

(C) y = 0.25 cos (t + 2x)

(D) y = 0.5 cos (t + x)

WAVES

171

13. The resultant amplitude, when two waves of same

frequency but with amplitudes a1 and a

2

superimpose at phase difference of /2 will be:–

(A) a1 + a

2(B) a

1 – a

2

(C) 2 21 2a a (D) 2 2

1 2a a

14. A source of sound is in the shape of a long narrowcylinder radiating sound waves normal to the axisof the cylinder. Two points P and Q are atperpendicular distances of 9 m and 25 m from theaxis. The ratio of the amplitudes of the waves at Pand Q is:–

(A) 5 : 3 (B) 5 : 3

(C) 3 : 5 (D) 25 : 9

15. The extension in a string, obeying Hooke's law,is x. The speed of sound in the stretched stringis v. If the extension in the string is increased to1.5x, the speed of sound will be:–

(A) 1.22 v (B) 0.61 v

(C) 1.50 v (D) 0.75 v

16. The ratio of intensities of two waves is 9 : 1. When

they superimpose, the ratio of maximum to minimum

intensity will become:–

(A) 4 : 1 (B) 3 : 1

(C) 2 : 1 (D) 1 : 1

17. The linear density of a vibrating string is 1.3 x 10–4 kg/m. A

transverse wave is propagating on the string and is

described by the equation y=0.021 sin (x+30t) where

x and y are measured in meter and t in second the

tension in the string is :–

(A) 0.12 N (B) 0.48 N

(C) 1.20 N (D) 4.80 N

18. A steel wire of length 60 cm and area of cross–

section 10–6 m2 is joined with an aluminium wire of

length 45 cm and area of cross–section 3×10–6m2.

The composite string is stretched by tension of 80 N.

Density of steel is 7800 kg m–3 and that of aluminium

is 2600 kg m–3. The minimum frequency of tuning

fork which can produce standing wave in it with

node at the joint is:–

A B C60cm

45cm

(A) 357.3 Hz (B) 375.3 Hz

(C) 337.5 Hz (D) 325.5 Hz

19. A copper wire is fixed between two rigid supports.

It is stretched with negligible tension at 30°C. The

speed of transverse waves in the wire at 10°C will

be– (density d = 9 × 103 kg/m3, Young's modulus

Y = 1.3 × 1011 N/m² and temperature coefficient of

expansion = 1.7 × 10–5 /°C):–

(A) 210 m/s (B) 110 m/s

(C) 90 m/s (D) 70 m/s

20. A wave pulse on a string has the dimension shown

in figure. The waves speed is v = 1 cm/s. If point

O is a free end. The shape of wave at time t=3s

is:–

1cm

1cm 1cm 2cm

v=1cm/s

O

(A)

(B) 1cm

1cm

O

(C)

1cm

1cm

O

(D)

1cm

2cm

O

21. A uniform rope having some mass hinges

vertically from a rigid support. A transverse wave

pulse is produced at the lower end. The speed (v)

of the wave pulse varies with height (h) from the

lower end as:–

(A)

V

h

(B)

V

h

(C)

V

h

(D)

V

h

172


22. The equation y = a sin 2/(vt – x) is expression

for:–

(A) Stationary wave of single frequency along x–

axis.

(B) A simple harmonic motion.

(C) A progressive wave of single frequency along

x–axis.

(D) The resultant of two SHM's of slightly different

frequencies.

23. A plane wave y = a sin (bx + ct) is incident on a

surface. Equation of the reflected wave is y' = a'

sin(ct–bx). Which of the following statements is

not correct ?

(A) The wave is incident on the surface normally.

(B) Reflecting surface is y–z plane.

(C) Medium, in which incident wave is travelling, is

denser than the other medium.

(D) a’ cannot be greater than a.

24. A wave is represented by the equation y = a sin(kx – t)

is superimposed with another wave to form a

stationary wave such that the point x = 0 is a node.

Then the equation of other wave is:–

(A) y = a cos (kx – t) (B) y = acos (kx + t)

(C) y = – asin (kx + t) (D) y = a sin (kx + t)

25. Stationary waves are produced in 10m long

stretched string. If the string vibrates in 5 segments

and wave velocity 20m/s then the frequency is:–

(A) 10 Hz (B) 5 Hz

(C) 4 Hz (D) 2Hz

26. A standing wave having 3 nodes and 2 antinodes is

formed between 1.21 Å distance then the wavelength

is:–

(A) 1.21 Å (B) 2.42 Å

(C) 0.605 Å (D) 4.84 Å

27. An object of specific gravity is hung from a thin

steel wire. The fundamental frequency for

transverse standing waves in the wire is 300 Hz.

The object is immersed in water, so that one half

of its volume is submerged. The new fundamental

frequency (in Hz) is:–

(A) 300

1 / 22 1

2

(B) 300

1 / 22

2 1

(C) 3002

2 1

(D) 3002 1

2

28. A string is cut into three parts, having fundamental

frequencies n1, n

2 and n

3 respectively. Then original

fundamental frequency 'n' related by the expression

as (other quantities are identical):–

(A) 1

n=

1

1

n+

2

1

n+

3

1

n(B) n = n

1 × n

2 × n

3

(C) n = n1 + n

2 + n

3(D) n =

1 2 3n n n

3

29. A thunder tap is heard 5.5 s after the lightening

flash. The distance of the flash is (velocity of sound

in air is 330 m/s):–

(A) 3560 m (B) 300 m

(C) 1780 m (D) 1815 m

30. Microwaves from a transmitter are directed

normally towards a plane reflector. A detector

moves along the normal to the reflector. Between

positions of 14 successive maxima, the detector

travels a distance 0.14m. If the velocity of light

is 3 × 108 m/s, find the frequency of the

transmitter:–

(A) 1.5 × 1010 Hz (B) 1010 Hz

(C) 3 × 1010 Hz (D) 6 × 1010 Hz

31. A tube, closed at one end and containing air,

produces, when excited, the fundamental note of

frequency 512 Hz. If the tube is opened at both

ends the fundamental frequency that can be

excited is (in Hz.):–

(A) 1024 (B) 512

(C) 256 (D) 128

32. At the room temperature the velocity of sound in

O2 gas is v. Then in mixture of H

2 and O

2 gas the

speed of sound at same temperature:–

(A) will be less than v. (B) will be more than v

(C) will be equal to v (D) nothing can be said

33. An underwater sonar source operating at a

frequency of 60 kHz directs its beam towards the

surface. If velocity of sound in air is 330 m/s,

wavelength and frequency of the waves in air are:–

(A) 5.5 mm, 60 kHz (B) 3.30 m, 60kHz

(C) 5.5 mm, 30 kHz (D) 5.5 mm, 80 kHz

WAVES

173

34. An organ pipe P1 closed at one end vibrating in

its first harmonic and another pipe P2 open at ends

vibrating in its third harmonic are in resonance

with a given tuning fork. The ratio of the length

of P1 and P

2 is:–

(A) 8

3(B)

3

8

(C) 1

6(D)

1

3

35. A cylindrical tube, open at both ends, has a

fundamental frequency ƒ in air. The tube is dipped

vertically in water so that half of its in water. The

fundamental frequency of the air column is now :–

(A) ƒ

2(B)

3ƒ

4

(C) ƒ (D) 2ƒ

36. The velocity of sound in air is 333 m/s. If the

frequency of the fundamental tone is 333 Hz, the

length of the open pipe to generate second

harmonic is:–

(A) 0.5m (B) 1.0m

(C) 2.0m (D) 4.0 m

37. An open pipe is suddenly closed at one end with

the result that the frequency of third harmonic of

the closed pipe is found to be higher by 100 Hz

than the fundamental frequency of the open pipe.

The fundamental frequency of the open pipe is:–

(A) 200 Hz (B) 300 Hz

(C) 240 Hz (D) 480 Hz

38. A cylindrical tube (L = 120 cm.) is in resonance with

a tuning fork of frequency 330 Hz. If it is filling by

water then to get resonance again, minimum length

of water column is (vair

= 330 m/s):–

(A) 45 cm (B) 60 cm

(C) 25 cm (D) 20 cm

39. The maximum length of a closed pipe that would

produce a just audible sound is (vsound

= 336 m/s):–

(A) 4.2 cm (B) 4.2 m

(C) 4.2 mm (D) 1.0 cm

40. Two vibrating tuning forks produce progressive

waves given by y1 = 4 sin 500t and y2 = 2 sin 506 t.

Number of beats produced per minute is:–

(A) 3 (B) 360

(C) 180 (D) 60

41. A closed organ pipe of radius r1 and an open organ

pipe of radius r2 and having same length 'L'

resonate when excited with a given tuning fork.

Closed organ pipe resonates in its fundamental

mode where as open organ pipe resonates in its

first overtone, then:–

(A) r2 – r

1 =L (B) r

2 = r

1 = L/2

(C) r2 – 2r

1 = 2.5 L (D) 2r

2 – r

1 = 2.5 L

42. Length of a sonometer wire is either 95 cm or 100

cm. In both the cases a tuning fork produces 4 beats

then the frequency of tuning fork is:–

(A) 152 (B) 156

(C) 160 (D) 164

43. Frequency of tuning fork A is 256 Hz. It produces 4

beats/second with tuning fork B. When wax is

applied at tuning fork B then 6 beats/second are

heard. Frequency of B is:–

(A) 250 Hz

(B) 260 Hz

(C) 252 Hz

(D) (A) & (C) both may possible

44. 16 tuning forks are arranged in increasing order of

frequency. Any two consecutive tuning forks when

sounded together produce 8 beats per second. If

the frequency of last tuning fork is twice that of

first, the frequency of first tuning fork is:–

(A) 60 (B) 80

(C) 100 (D) 120

45. Two open pipes of length 25 cm and 25.5 cm

produced 0.1 beat/second. The velocity of sound

will be:–

(A) 255 cm/s (B) 250 cm/s

(C) 350 cm/s (D) none of these

46. Two open pipes of length L are vibrated

simultaneously. If length of one of the pipes is

reduced by y, then the number of beats heard per

second will be if the velocity of sound is v and y

<< L:–

(A) 2

vy

2L(B) 2

vy

L

(C) vy

2L(D)

22L

vy

174


47. Two tuning forks having frequency 256 Hz (A) and

262 Hz (B) tuning fork. A produces some beats per

second with unknown tuning fork, same unknown

tuning fork produce double beats per second from

B tuning fork then the frequency of unknown tuning

fork is:–

(A) 262 (B) 260

(C) 250 (D) 300

48. A sound absorber attenuates the sound level by

20 dB. The intensity decreases by a factor of:–

(A) 1000 (B) 10000

(C) 10 (D) 100

49. The power of sound from the speaker of a radio is

20MW by turning the knob of the volume control

the power of the sound is increased to 400 MW.

The power increase in describe as compared to the

original power is :–

(A) 13 dB (B) 10 dB

(C) 20 dB (D) 800 dB

50. A person observes a change of 2.5% in frequency

of sound of horn of a car. If the car is approaching

forward the person & sound velocity is 320 m/s,

then velocity of car in m/s will be approximately:–

(A) 8 (B) 800

(C)7 (D) 6

51. A whistle giving out 450 Hz approaches a

stationary observer at a speed of 33 m/s. The

frequency heard by the observer (in Hz) is : (speed

of sound 333 m/s)

(A) 409 (B) 429

(C) 517 (D) 500

52. A whistle revolves in a circle with angular speed =

20 rad/s using a string of length 50 cm. If the

frequency of sound from the whistle is 385 Hz, then

what is the minimum frequency heard by an observer

which is far away from the centre:–

(vsound

= 340 m/s)

(A) 385 Hz (B) 374 Hz

(C) 394 Hz (D) 333 Hz

53. Two trains A and B are moving in the same direction

with velocities 30 m/s and 10 m/s respectively, B is

behind from A, blows a horn of frequency 450 Hz.

Then the apparent frequency heard by B is (The

velocity of sound is 330 m/s):–

(A) 425 Hz (B) 300 Hz

(C) 450 Hz (D) 350 Hz

WAVES

175

Exercise # 3 PART - 1 MATRIX MATCH COLUMN

1. Column I Column II

(A) y = 4sin(5x–4t)+3cos(4t–5x+/6) (P) Particles at every position are performing SHM

(B) y = 10cosx

t330

sin(100)

xt

330

(Q) Equation of travelling wave

(C) y=10sin(2x–120t)+10cos(120t+2x) (R) Equation of standing wave

(D) y=10sin(2x–120t)+8cos(118t–59/30x) (S) Equation of Beats

2. From a single source, two wave trains are sent in two different strings. Strings–2 is 4 times heavy than string–1. The two

wave equations are : (area of cross–section and tension of both strings is same) y1 = A sin (

1t – k

1x) and y

2 = 2A sin

(2t – k

2x). Suppose u= energy density, P=power transmitted and I=intensity of the wave.

Column I Column II

(A) u1/u

2 is equal to (P) 1/8

(B) P1/P

2 is equal to (Q) 1/16

(C) I1/I

2 is equal to (R) 1/4


(A) Interference (P) Intensity varies periodically with time

(B) Beats (Q) Intensity varies periodically with position

(C) Echo (R) Reflection of waves

(S) Refraction of waves


(A) Infrasonic (P) Speed is greater than speed of sound

(B) Ultrasonic (Q) Frequency < 20 Hz

(C) Audible (sonic) (R) Frequency > 20 kHz

(D) Supersonic (S) 20 Hz < frequency < 20 kHz


(A) Pitch (P) Number of overtones

(B) Quality (Q) Intensity

(C) Loudness (R) Frequency

(D) Musical interval (S) Difference of the frequencies of two notes

(T) Ratio of the frequencies of two notes

176


Exercise # 3 PART - 2 ASSERTION & REASONING

These questions contains, Statement I (assertion)

and Statement II (reason).

(A) If both assertion and reason are true and the

reason is the correct explanation of the

assertion.

(B) If both assertion and reason are true but

reason is not the correct explanation of the

assertion.

(C) If assertion is true but reason is false.

(D) If assertion is false but reason is true.

(E) If the assertion and reason both are false.

1. Assertion : Two persons on the surface of moon

cannot talk to each other.

Reason : There is no atmosphere on moon.

2. Assertion : Transverse waves are not produced in

liquids and gases.

Reason : Light waves are transverse waves.

3. Assertion : The change in air pressure effects the

speed of sound.

Reason : The speed of sound in gases is proportional

to the square of pressure.

4. Assertion : The reverberation time dependent on

the shape of enclosure, position of source and

observer.

Reason : The unit of absorption coefficient in mks

system is metric sabine.

5. Assertion : When a beetle moves along the sand

with in a few tens of centimeters of a sand scorpion

the scorpion immediately turn towards the beetle

and dashes to it

Reason : When a beetle disturbs the sand, it sends

pulses along the sands surface one set of pulses is

logitudinal while other set is transverse.

6. Assertion : Transverse waves travel through air in

an organ pipe.

Reason : Air possesses only volume elasiticity.

7. Assertion : Sound would travel faster on a hot

summer day than on a cold winter day.

Reason : Velocity of sound is directly proportional

to the square of its absolute temperature.

8. Assertion : The basic of Laplace correction was

that, exchange of heat between sthe region of

compression and rarefaction in air is not possible.

Reason : Air is bad conductor of heat and velocity

of sound in air large.

9. Assertion : Particle velocity and wave velocity both

are independent of time.

Reason : For the propagation of wave motion, the

medium must have the properties of elasticity and

inertia.

10. Assertion : The flash of lightening is seen before

the sound of thunder is heard.

Reason : Speed of sound is greater than speed of

light

11. Assertion : A tuning fork is made of an alloy of

steel, nickel and chromium.

Reason : The alloy of steel, nickel and chromium is

called elinvar.

12. Assertion : The change in air pressure effect the

speed of sound.

Reason : The speed of sound in a gas is proportional

to square root of pressure.

13. Assertion : Solids can support both longitudinal

and transverse waves but only longitudinal waves

can propagate in gases.

Reason : For the propagation of transverse waves,

medium must also necessarily have the propoerty

of rigidity.

14. Assertion : Under given conditions of pressure and

temperature, sound travels faster in a monoatomic

gas than in diatomic gas.

Reason : Opposition for wave to travel is more ini

diatomic gas than monoatomic gas.

15. Assertion : The speed of sound in solids is maximum

though their density is large.

Reason : The coefficient of elasticity of solids is

large.

16. Assertion : On a rainy day sound travels slower

than on a dry day.

Reason : When moisture is present in air the density

of air increases.

WAVES

177

17. Assertion : Seed of wave = Wave length

Time period

Reason : Wavelength is the distance between two

nearest particle in phase.

18. Assertion : Sound produced by an open organ pipe

is richer than the sound produced by a closed organ

pipe.

Reason : Outside air can enter the pipe from both

ends, in case of open organ pipe.

19. Assertion : It is not possible to have interference

between the waves produced by two violins.

Reason : For interference of two waves the phase

difference between the waves must remain constant.

20. Assertion : Like sound, light can not propagate in

vacuum.

Reason : Sound is a square wave. It propagates in

medium by a virtue of damping oscillation.

21. Assertion : In the case of stationary wave, a person

hear a loud sound at the nodes as compared to the

antinodes.

Reason : In a stationary wave all the particles of the

medium vibrate in phase.

22. Assertion : Velocity of particles, while crossing

mean position (in stationary waves) varies from

maximum at antinodes to zero at nodes.

Reason : Amplitude of vibtration at antinodes is

maximum and at nodes, the amplitude is zero, And

all particles between two successive nodes cross

the mean position together.

23. Assertion : Where two vibrating tuning forks

having frequencies 256 Hz and 512 Hz are held near

each other, beats cannot be heard.

Reason : The principle of superposition is valid only

if the frequencies of the oscillators are nearly equal.

24. Assertion : The fundamental frequency of an open

organ pipe increases as the temperature is increased.

Reason : As the temperature increases, the velocity

of sound increases more rapidly than length of the

pipe.

25. Assertion : Sound travels faster in solids than

gases.

Reason : Solid posses greater density than gases.

178


Exercise # 4 PART - 1 PREVIOUS YEAR (NEET/AIPMT)

1. Two sources are at a finite distacne apart. They

emit sounds of wavelength . An observer situated

between them on line joining approaches one source

with speed u. Then, the number of beat heart/second

by observer will be [CBSE AIPMT 2000]

(A) 2u

(B)

u

(C) u

(D)

u

2. A sonometer wire when vibrated in full length has

frequency n. Now, it is divided by the help of bridges

into a number of segments of lengths l1, l

2, l

3, ...

When vibrated these segments have frequencies

n1, n

2, n

3, ... The, the correct, relation is

[CBSE AIPMT 2000]

(A) n = n1 + n

2 + n

3 + .....

(B) n2 = n

12 + n

22 + n

32 + ....

(C) 1 2 3

1 1 1 1....

n n n n

(D) 1 2 3

1 1 1 1....

n n n n

3. Two strings A and B have lengths lA and l

B and

carry masses MA and M

B at their lower ends, the

upper ends being supported by rigid supports. If

nA and n

B are the frequencies of their vibrations and

nA = 2 n

B, then [CBSE AIPMT 2000]

(A) lA = 4l

B, regardless of masses

(B) lB = 4l

A, regardless of masses

(C) MA = 2 M

B, l

A = 2l

B

(D) MB = 2 M

A, l

B = 2 l

A

4. Equations of two progressive waves are given by

y1 = a sin (t +

1) and y

2 = a sin (t +

2). If amplitude

and time period of resultant wave are same as that

of both the waves, then (1 –

2) is

[CBSE AIPMT 2001]

(A) 3

(B)

3

(C) 6

(D)

4

5. A wave enters to water from air. In air frequency,

wavelength, intensity and velocity are n1,

1 and v

1

respectively. In water the corresponding quantities

are n2, l

2, I

2 and v

2 respectively, then

[CBSE AIPMT 2001]

(A) l1 = l

2(B) n

1 = n

2

(C) v1 = v

2(D)

1 =

2

6. The equation of a wave is given by

xy asin 100t

10

, where x and y are in metre

and t in second, then velocity of wave is

[CBSE AIPMT 2001]

(A) 0.1 m/s (B) 10 m/s

(C) 100 m/s (D) 1000 m/s

7. A wave of amplitude a = 0.2 m, velocity v = 360 m/s

and wavelength 60 m is travelling along positive x-

axis, then the correct expression for the wave is

[CBSE AIPMT 2002]

(A) y 0.2sin 2 6t60

(B) x

y 0.2sin 6t60

(C) x

y 0.2sin 2 6t60

(D) x

y 0.2sin 6t60

8. A whistle revolves in a circle with angular velocity

= 20 rad/s using a string of length 50 cm.If the

actual frequency of sound from the whistle is 385

Hz, then the minimum frequency heard by the

observer far away from the centre is (velocity of

sound v = 340 m/s) [CBSE AIPMT 2002]

(A) 385 Hz (B) 374 Hz

(C) 394 Hz (D) 333 Hz

WAVES

179

9. An observer moves towards a stationary source of

sound with a speed 1

th5

of the speed of sound. the

wavelength and frequency of the source emitted

are and f respectively. The apparent frequency

and wavelength recorded by the observer are

respectively [CBSE AIPMT 2003]

(A) f, 1.2 (B) 0.8f, 0.8

(C) 1.2f, 1.2 (D) 1.2f,

10. A car is moving towards a high cliff. The car driver

sounds a horn of frequency f. The reflected sound

heard by the driver has a frequency 2f. If v be the

velocity of sound, then the velocity of the car, in

the same velocity units, will be

[CBSE AIPMT 2004]

(A) v

2(B)

v

3

(C) v

4(D)

v

2

11. The phase difference between two waves,

represented by

6

1

xy 10 sin 100 t 0.5 m

50

6

2

xy 10 cos 100 t m

50

where, x is expressed in metre and t is expressed in

second, is approximately [CBSE AIPMT 2004]

(A) 1.07 rad (B) 2.07 rad

(C) 0.5 rad (D) 1.5 rad

12. A point source emits sound equally in all directions

in a non-absorbing medium. Two point P and Q are

at distance of 2m and 3m respectively from the

source. The ratio of the intensities of the waves at P

and Q is [CBSE AIPMT 2005]

(A) 9 : 4 (B) 2 : 3

(C) 3 : 2 (D) 4 : 9

13. Two vibrating tuning forks produce progressive

waves given by

y1 = 4 sin 500 t and y

2 = 2 sin 506 t.

Number of beat produced per minute is

[CBSE AIPMT 2005]

(A) 360 (B) 180

(C) 3 (D) 60

14. Two sound waves with wavelengths 5 m and 5.5 m

respectively, each propagate in a gas with velocity

330 m/s. We expect the following number of beat

per second

(A) 12 (B) zero

(C) 1 (D) 6

15. A transverse wwave propagating along x-axis is

represented by

y(x, t) 8sin 0.5 x 4 t4

where, x is in metre and t is in second.

The speed of the wave is

[CBSE AIPMT 2006]

(A) 4 m/s (B) 0.5 m/s

(C) m / s4

(D) 8 m/s

16. The time of reverberation of a room A is 1s. What

will be the time (in second) of reverberation of a

room, having all the dimensions double of those of

room A? [CBSE AIPMT 2006]

(A) 2 (B) 4

(C) 1

2(D) 1

17. Which one of the following statements is true?

[CBSE AIPMT 2006]

(A) Both light and sound waves in air are transverse

(B) The sound waves in air are longitudinal while

the light waves are transverse

(C) Both light and sound waves in air are

longitudinal

(D) Both light and sound waves can travel in

vacuum

18. Two periodic wavves of intensities I1 and I

2 pass

through a region at the same time in the same

direction. The sum of the maximum and minimum

intensities is [CBSE AIPMT 2008]

(A) l1 + l

2(B) 2

1 2( l l )

(C) 2

1 2( l l ) (D) 2 (l1 + l

2)

180


19. The wave described by y = 0.25 sin (10 px – 2t),

where, x and y are in metre and t in second, is a wae

travelling along the [CBSE AIPMT 2008]

(A) negative x-direction with frequency 1 Hz

(B) positive x-direction with frequency Hz and

wavelength = 0.2 m

(C) positive x-direction with frequency 1 Hz and

wavelength = 0.2 m

(D) negative x-direction with amplitude 0.25 m and

wavelength = 0.2 m

20. A wave in a string has an amplitude of 2cm. The

wave travels in the positive direction of x-axis with

a speed of 128 ms–1 and it is noted that 5 complete

waves fit in 4 m length of the string. The equation

describing the wave is

[CBSE AIPMT 2009]

(A) y = (0.02) m sin(7.85 x + 1005 t)

(B) y = (0.02) m sin (15.7 x – 2010t)

(C) y = (0.02(m sin (15.7 x + 2010t)

(D) y = (0.02) m sin (7.85 x – 1005 t)

21. The driver of a car travelling with speed 30 ms–1

towards a hill sounds a horn of frequency 600 Hz. If

the velocity of sound in air is 330 ms–1, the frequency

of reflected sound as heard by driver is

[CBSE AIPMT 2009]

(A) 550 Hz (B) 555.5 Hz

(C) 720 Hz (D) 500 Hz

22. A tuning fork of frequency 512 Hz makes 4 beat/s

with the vibrating string of a piano. The beat

frequency decreases to 2 beat/s when the tension

in the piano string is slightly increased. The

frequency of the piano string before increasing the

tension was [CBSE AIPMT 2010]

(A) 510 Hz (B) 514 Hz

(C) 516 hz (D) 508 Hz

23. A transverse wave is represented by y = A sin (t – kx).

For what value of the wavelength is the wave

velocity equal to the maximum particle velocity ?

[CBSE AIPMT 2010]

(A) A/2 (B) A

(C) 2 A (D) A

24. Sound waves travel at 350 m/s through a warm air

and at 3500 m/s through brass. The wavelength of a

700 Hz acoustic wave as it enters brass from warm

air [CBSE AIPMT 2011]

(A) increases by a factor 20

(B) increases by a factor 10

(C) decreases by a factor 20

(D) decreases by a factor 10

25. Two waves are represented by the equations y1 = a

sin (t + kx + 0.57) m and y2 = a cos (t + kx) m,

where x is in metre and t in second. The phase

difference between them is [CBSE AIPMT 2011]

(A) 1.25 rad (B) 1.57 rad

(C) 0.57 rad (D) 1 rad

26. Two sources of sound placed closed to each other,

are emitting progressive waves given by y1 = 4 sin

600t and y2 = 5 sin 608 t . An observer located

near these two sources of sound will hear

[CBSE AIPMT 2012]

(A) 4 beat/s with intensity ratio 25 : 16 between

waxing and waning

(B) 8 beat/s with intensity ratio 25 : 16 between

waxing and waning

(C) 8 beat/s with intensity ratio 81 : 1 between

waxing and waning

(D) 4 beat/s with intensity ratio 81 : 1 between

waxing and waning

27. When a strin is divided into three segments of

lengths l1, l

2 and l

3, the fundamental frequencies of

these three segments are 1,

2 and

3 respectively.

The original fundamental frequency () of the string

is [CBSE AIPMT 2012]

(A) 2 3

(B) = 1 +

2 +

3

(C) 1 2 3

1 1 1 1

(D) 1 2 3

1 1 1 1

28. A source of unknown frequency gives 4 beats/s

when sounded with a source of known frequency

250 Hz. The second harmonic of the source of

unknown frequency gives five beats per second,

when sounded with a source of frequency 513 Hz.

The unknown frequency is [NEET 2013]

(A) 240 Hz (B) 260 Hz

(C) 254 Hz (D) 246 Hz

WAVES

181

29. A wave travelling in the +ve x-direction having

displacement along y-direction as 1 m, wavelength

2 m and frequency of 1

Hz is represented by

[NEET 2013]

(A) y = sin(10x – 20t) (B) y = sin(2x + 2t)

(C) y = sin(x – 2t) (D) y = sin(2x – 2t)

30. If we study the vibration of a pipe open at both

ends, then the following statement is not true.

[NEET 2013]

(A) All harmonics of the fundamental frequency

will be generated.

(B) Pressure change will be maximum at both ends.

(C) Open end will be antinode.

(D) Odd harmonics of the fundamental frequency

will be generated.

31. A speeding motorcyclist sees traffic jam ahead him.

He slows down to 36 km hour–1. He finds that traffic

has eased and a car moving ahead of him at 18 km

hour–1 is honking at a frequency of 1392 Hz. If the

speed of sound is 343 m s–1, the frequency of the

honk as heard by him will be [AIPMT 2014]

(A) 1332 Hz (B) 1372 Hz

(C) 1412 Hz (D) 1454 Hz

32. The number of possible natural oscillations of air

column in a pipe closed at one end of length 85 cm

whose frequencies lie below 1250 Hz are (Velocity

of sound = 340 m s–1) [AIPMT 2014]

(A) 4 (B) 5

(C) 7 (D) 6

33. If n1, n

2 and n

3 are the fundamental frequencies of

three segments into which a string is divided, then

the original fundamental frequency n of the string

is given by [AIPMT 2014]

(A) 1 2 3

1 1 1 1

n n n n

(B) 1 2 3

1 1 1 1

n n n n

(C) 1 2 3n n n n

(D) n = n1 + n

2 + n

3

34. A source of sound 5 emitting waves of frequency

100 Hz and an observer O are located at some

distance from each other. The source is moving with

a speed of 19.4 ms–1 at an angle of 60° with the

source observer line as shown in the figure. The

observer is at rest. The apparent frequency

observed by the observer (velocity of sound in air

is 330 ms–1), is [CBSE AIPMT 2015]

60°

S O

vs

(A) 100 Hz (B) 103 Hz

(C) 106 Hz (D) 97 Hz

35. The fundamental frequency of a closed organ pipe

of length 20 cm is equal to the second overtone of

an organ pipe open at both the ends. The length of

organ pipe open at both the ends is

[CBSE AIPMT 2015]

(A) 80 cm (B) 100 cm

(C) 120 cm (D) 140 cm

36. Three sound waves of equal amplitudes have

frequencies (n – 1, n, (n + 1). They superimpose to

give beats. The number of beats produced per

second will be [NEET 2016]

(A) 1 (B) 4

(C) 3 (D) 2

37. The second overtone of an open organ pipe has

the same frequency as the first overtone of a closed

pipe L metre long. The length of the open pipe will

be [NEET 2016]

(A) L (B) 2 L

(C) L/2 (D) 4L

38. A uniform rope of length L and mss m1 hangs

vertically from a rigid support. A block of mass m2 is

attached to the free end of the rop. A transverse

pulse of wavelength 1 is produced at the lower end

of the rope. The wavelength of the pulse when it

reaches the top of the rope is 2. The ratio

2/

1 is

[NEET 2016]

(A) 1 2

2

m m

m

(B)

2

1

m

m

(C) 1 2

1

m m

m

(D)

1

2

m

m

182


39. A siren emitting a sound of frequency 800 Hz moves

away from an observer towards a cliff at a speed of

15ms–1. Then, the frequency of sound that the

observer hears in the echo reflected from the cliff is

[Take, velocity of sound in air = 330 ms–1]

[NEET 2016]

(A) 800 Hz (B) 838 Hz

(C) 885 Hz (D) 765 Hz

40. Two cars moving in opposite directions approach

each other with speed of 22 m/s and 16.5 m/s

respectively. The driver of the first car blos a horn

having a frequency 400 Hz. The frequency heard

by the driver of the second car is [velocity of second

340 m/s] [NEET 2017]

(A) 350 Hz (B) 361 Hz

(C) 411 Hz (D) 448 Hz

41. The two nearest harmonics of a tube closed at one

end and open at other end are 220 Hz and 260 Hz.

What is the fundamental frequency of the system?

[NEET 2017]

(A) 10 Hz (B) 20 Hz

(C) 30 Hz (D) 40 Hz

WAVES

183

Exercise # 4 PART - 2 PREVIOUS YEAR (AIIMS)

1. Ratio of intensities of two waves is 9 : 1. If these

two are superimposed, what is the ratio of maximum

and minimum intensities ? [2000]

(A) 9 : 1 (B) 3 : 1

(C) 4 : 1 (D) 5 : 3

2. A transverse stationary waves passes through a

string with the equation y = 10sin(0.02x – 2.00t)

where x is in meters and t in seconds. The maximum

velocity of the particles in waves motion is [2000]

(A) 63 (B) 78

(C) 100 (D) 121

3. If fundamental frequency is 50 Hz and next

successive frequencies are 150 Hz and 250 Hz then

it is [2001]

(A) a pipe closed at both end

(B) a pipe closed at one end

(C) an open pipe

(D) a stretched pipe.

4. A source of frequency 240 Hz is moving towards an

observer with a velocity of 20 m/s. The observer is

now moving towards the source with a velocity of

20 m/s. Apparent frequency heard by observer, if

velocity of sound is 340 m/s, is [2001]

(A) 268 Hz (B) 270 Hz

(C) 360 Hz (D) 240 Hz.

5. A string in a musical instrument is 50 cm long and

its fundamental frequency is 800 Hz. If a frequency

of 1000 Hz is to be produced, then required length

of string is [2002]

(A) 62.5 cm (B) 40 cm

(C) 50 cm (D) 37.5 cm

6. If equation of sound wave is y = 0.0015sin(62.4x + 316t),

then its wavelength will be [2002]

(A) 0.2 unit (B) 0.3 unit

(C) 0.1 unit (D) 2 unit

7. The graph between wave number ( ) and angularfrequency () is [2002]

(A) Ang

ular

(B) Ang

ula

r(C) A

ng

ular

(D) Ang

ular

8. The velocities of sound at the same temperature intwo monoatomic gases of densities r

1 and r

2 are v

1

v2 respectively. If r

1/r

2 = 4, then the value of v

1/v

2 is

(A) 1/4 (B) 2 [2002]

(C) 1/2 (D) 4

9. An earthquake generates both transverse (S) and

longitudinal (P) sound waves in the earth. The speed

of S waves is about 4.5 km/s and that of P waves is

about 8.0 km/s. A seismograph records P and S

waves from an earthquake. The first P wave arrives

4.0 min before the first S wave. The epicentre of the

earthquake is located at a distance about [2003]

(A) 25 km (B) 250 km

(C) 2500 km (D) 500 km.

184


10. The waves produced by a motorboat sailing in water

are [2004]

(A) transverse

(B) longitudinal

(C) longitudinal and transverse

(D) stationary.

11. An organ pipe closed at one end has fundamental

frequency of 1500 Hz. The maximum number of

overtones generated by this pipe which a normal

person can hear is [2004]

(A) 14 (B) 13

(C) 6 (D) 9

12. A stone thrown into still water, creates a circular

wave pattern moving radially outwards. If r is the

distance measured from the centre of the pattern,

the amplitude of the wave varies as [2006]

(A) r–1/2 (B) r–1

(C) r–2 (D) r–3/2

13. A boat at anchor is rocked by waves whose crests

are 100 m apart and velocity is 25 m/sec. The boat

bounces up once in every [2006]

(A) 2500 s (B) 75 s

(C) 4 s (D) 0.25 s

14. When a guitar string is sounded with 440 Hz tuning

fork, a beat frequency of 5 Hz is heard. If the

experiment is repeated with a tuning fork of 437 Hz,

the beat frequency is 8 Hz. The string frequency

(Hz) is [2006]

(A) 445 (B) 435

(C) 429 (D) 448

15. For a wave propagating in a medium, identify the

property that is independent of the others.

(A) velocity [2006]

(B) wavelength

(C) frequency

(D) all these depend on each other

16. A siren emitting sound of frequency 800 Hz is going

away from a static listener with a speed of 30 m/s.

Frequency of the sound to be heard by the listener

is (Take velocity of sound as 330 m/s) [2002, 2007]

(A) 733.3 Hz (B) 481.2 Hz

(C) 644.8 Hz (D) 286.5 Hz.

17. Two closed organ pipes of length 100 cm and 101cm produced 16 beats in 20 sec. When each pipe issounded in its fundamental mode calculate thevelocity of sound. [2008]

(A) 303 ms–1 (B) 332 ms–1

(C) 323.2 ms–1 (D) 300 ms–1

18. A uniform string is vibrating with a fundamentalfrequency ‘f’. The new frequency, if radius andlength both are doubled would be [2010]

(A) 2f (B) 3f

(C) 4

f(D)

3

f

19. Five sinusoidal waves have the same frequency 500

Hz but their amplitudes are in the ratio 1 1

2 : : :1:12 2

and their phase angles 0, , ,6 3 2

and

respectively. The phase angle of resultant waveobtained by the superposition of these five wavesis [2010]

(A) 30° (B) 45°

(C) 60° (D) 90°

20. The second overtone of an open pipe has the samefrequency as the first overtone of a closed pipe 2 mlong. The length of the open pipe is [2010]

(A) 8 m (B) 4 m

(C) 2 m (D) 1 m

21. What is your observation when two sources are

emitting sound with frequency 499 Hz and 501 Hz ?

(A) Frequency of 500 Hz is heard with change in

intensity take place twice. [2011]

(B) Frequency of 500 Hz is heard with change in

intensity take place once.

(C) Frequency of 2 Hz is heard with change in

intensity take place once.

(D) Frequency of 2 Hz is heard with change in

intensity take place twice.

22. If man were standing unsymmetrically between

parallel cliffs, claps his hands and starts hearing a

series of echoes at intervals of 1 s. If speed of sound

in air is 340 m s–1, the distance between two cliffs

would be [2011]

(A) 340 m (B) 510 m

(C) 170 m (D) 680 m

WAVES

185

23. Two sinusoidal waves of intensity I having same

frequency and same amplitude interferes

constructively at a point. The resultant intensity at

a point will be [2012]

(A) I (B) 2I

(C) 4I (D) 8I

24. Two waves represented by y = asin(t – kx) and

y = acos(t – kx) are superposed. The resultant

wave will have an amplitude [2014]

(A) a (B) 2a

(C) 2a (D) zero

25. A 5.5 metre length of string has a mass of 0.0035 kg.

If the tension in the string is 77 N, the velocity of

the wave on the string is [2014]

(A) 210 m s–1 (B) 40 m s–1

(C) 100 m s–1 (D) 55 m s–1

26. The equation of a progressive wave is given by

y = 5 sin(100t – 0.4x) where y and x are in m ant t

is in s. [2015]

(1) The amplitude of the wave is 5 m.

(2) The wavelength of the wave is 5 m.

(3) The frequency of the wave is 50 Hz.

(4) the velocity of the wave is 250 m s–1.

Which of the following statements are correct ?

(A) (1), (2) and (3) (B) (2) and (3)

(C) (1) and (4) (D) All are correct

27. The displacement of a particle executing SHM is

given by y = 0.25sin200t cm. The maximum speed of

the particle is [2016]

(A) 200 cm s–1 (B) 100 cm s–1

(C) 50 cm s–1 (D) 5.25 cm s–1

28. A wave is represented by the equation

y = 0.5 sin(10t – x) metre It is a travelling wave

propagating along + x direction with velocity

(A) 10 m s–1 (B) 20 m s–1 [2016]

(C) 5 m s–1 (D) None of these

ASSERTION AND REASON

29. Assertion : The flash of lightening is seen before

the sound of thunder is heard.

Reason : Speed of sound is greater than speed of

light. [2002]

30. Assertion : When a beetle move along the sand

within a few tens of centimeters of a sand scorpion,

the scorpion immediately turns towards the beetle

and dashes towards it.

Reason : when a beetle disturbs the sand, it sends

pulses along the sand’s surface. One set of pulses

is longitudinal while the other set is transverse.

[2003]

31. Assertion : Sound waves cannot propagate

through vacuum but light waves can.

Reason : Sound waves cannot be polarised but light

waves can be. [1997, 2007]

32. Assertion : In the relation 1 T

,2

fl

where

symbols have standard meaning, represents linear

mass density.

Reason : The frequency has the dimensions of

inverse of time. [2008]

33. Assertion : Transverse sound wave does not occurs

in gases.

Reason : Gases cannot sustain shearing strain.

[2011]

34. Assertion : To hear distinct beats, difference in

frequencies of two sources should be less than 10.

Reason : More the number of beats per sec more

difficult to hear them. [2014]

35. Assertion : The fundamental frequency of an open

organ pipe increases as the temperature is increased.

Reason : This is because as the temperature

increases, the velocity of sound increases more

rapidly than length of the pipe. [2015]

186


MOCK TEST

STRAIGHT OBJECTIVE TYPE

1. A travelling wave y = A sin (k x

t + ) passes from a heavier string to a lighter string. The reflected wave has

amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:

(A) y = 0.5 A sin (k

x +

t + ) (B) y

= 0.5 A sin (k

x +

t + )

(C) y = 0.5 A sin (

t k

x ) (D) y

= – 0.5 A sin (k

x +

t )

2. Which of the following travelling wave will produce standing wave, with node at x = 0, when superimposed on

y = A sin ( t k

x)

(A) A sin ( t + k

x) (B) A sin (

t + k

x + )

(C) A cos ( t + k

x) (D) A cos (

t + k

x + )

3. A wire of length ‘ ‘ having tension T and radius ‘

r

‘ vibrates with fundamental frequency ‘

f

‘. Another wire

of the same metal with length ‘ 2 ‘ having tension 2

T and radius 2

r will vibrate with fundamental frequency:

(A) f (B) 2 f (C)

22

f(D)

2

f2

4. A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre

of the string is 4 mm. Distances between the two points having amplitude 2 mm is:

(A) 1 m (B) 75 cm (C) 60 cm (D) 50 cm

5. Two particles of medium disturbed by the wave propagation are at x1 = 0 and x

2 = 1cm. The respective

displacements (in cm) of the particles can be given by the equations :

y1 = 2sin3t

y2 = 2sin(3t – /8)

The wave velocity is :

(A) 16 cm/sec (B) 24 cm/sec (C) 12 cm/sec (D) 8 cm/sec.

6. The displacement Vs time graph for two waves A and B which travel along the same string are shown in the

figure. Their intensity ratio A /B is

1 2 3 4 5 6 7 8 9 10 11 12

B

t

A3

Y

0

(A) 4

9(B) 1 (C)

16

81(D)

2

3

7. At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is

described by the function y = 2x

6, given that x 0. Transverse velocity of a particle at x = 2m and

t = 2 seconds is :

(A) 3 m/s (B) – 3 m/s (C) 8 m/s (D) – 8 m/s

WAVES

187

8. Wave pulse on a string shown in figure is moving to the right without changing shape. Consider two particles

at positions x1 = 1.5 m and x

2 = 2.5 m. Their transverse velocities at the moment shown in figure are along

directions :

1 2 3 4 5 6x(m)

v

y

(A) positive y–axis and positive y–axis respectively

(B) negative y–axis and positive y–axis respectively

(C) positive y–axis and negative y–axis respectively

(D) negative y–axis and negative y–axis respectively

9. A wave pulse is generated in a string that lies along x-axis. At the points A and B, as shown in figure, if RA and

RB are ratio of wave speed to the particle speed respectively then :

A

B V

y

x

(A) RA > R

B(B) R

B > R

A

(C) RA = R

B(D) Information is not sufficient to decide.

10. Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to

4.00 × 10–2 kg/m. If the source can deliver a average power of 90 W and the string is under a tension of 100 N,

then the highest frequency at which the source can operate is (take 2 = 10) :

(A) 45.3 Hz (B) 50 Hz (C) 30 Hz (D) 62.3 Hz

11. The figure shows four progressive waves A, B, C & D. It can be concluded from the figure that with respect to wave A:

(A) the wave C is ahead by a phase angle of /2 & the wave B lags behind by a phase angle /2

(B) the wave C lags behind by a phase angle of /2 & the wave B is ahead by a phase angle of /2

(C) the wave C is ahead by a phase angle of& the wave B lags behind by the phase angle of

(D) the wave C lags behind by a phase angle of & the wave B is ahead by a phase angle of

12. A 75 cm string fixed at both ends produces resonant frequencies 384 Hz and 288 Hz without there being any

other resonant frequency between these two. Wave speed for the string is :

(A) 144 m/s (B) 216 m/s (C) 108 m/s (D) 72 m/s

188


13. A closed organ pipe has length ‘ ‘. The air in it is vibrating in 3rd overtone with maximum amplitude ‘

a‘.

Find the amplitude at a distance of /7 from closed end of the pipe.

(A) a (B) a/2 (C) 3 a/2 (D) a/ 2

14. When a sound wave is reflected from a wall, the phase difference between the reflected and incident pressure

wave is:

(A) 0 (B) (C) /2 (D) /4

15. A source of frequency 'f' is stationary and an observer starts moving towards it at t = 0 with constant small

acceleration. Then the variation of observed frequency f ' registered by the observer with time is best

represented as :

(A)

t

f�

(B)

t

f�

(C)

t

f�(D)

t

f�

16. A stationary observer receives sonic oscillations from two tuning forks, one of which approaches and the

other recedes with same speed. As this takes place the observer hears the beat frequency of 2 Hz. Find the

speed of each tuning fork, if their oscillation frequency is 680 Hz and the velocity of sound in air is 340 m/s.

(A) 1 m/s (B) 2 m/s (C) 0.5 m/s (D) 1.5 m/s

17. A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of

5 m/sec. If sound travels at a speed of 330 m/sec, then number of beats per second heard by an observer

between the wall and the source is:

(A) 7.7 Hz (B) 9 Hz (C) 4 Hz (D) none of these

18. A point source is emitting sound in all directions. The ratio of distance of two points from the point source

where the difference in loudness levels is 3 dB is: (log10

2 = 0.3)

(A) 2

1(B)

2

1(C)

4

1(D)

3

2

19. Two coherent sources of different intensities send waves which interfere. The ratio of the maximum intensity

to the minimum intensity is 25. The intensities are in the ratio:

(A) 25: 1 (B) 5: 1 (C) 9: 4 (D) 625: 1

20. The frequency of a man’s voice is 300 Hz and its wavelength is 1 meter. If the wavelength of a child’s voice is

1.5 m, then the frequency of the child’s voice is:

(A) 200 Hz (B) 150 Hz (C) 400 Hz (D) 350 Hz.

21. A sound wave of frequency 440 Hz is passing through air. An O2 molecule (mass = 5.3 1026 kg) is set in

oscillation with an amplitude of 106 m. Its speed at the centre of its oscillation is:

(A) 1.70 105 m/s (B) 17.0 105 m/s (C) 2.76 103 m/s (D) 2.77 105 m/s

WAVES

189

22. In the figure shown a source of sound of frequency 510 Hz moves with

constant velocity vs = 20 m/s in the direction shown. The wind is blowing

at a constant velocity vw = 20 m/s towards an observer who is at rest at

point B. Corresponding to the sound emitted by the source at initial position

A, the frequency detected by the observer is equal to (speed

of sound relative to air = 330 m/s)

30°

yvs

vw

A Bx

(A) 510 Hz (B) 500 Hz

(C) 525 Hz (D) 550 Hz

23. A wall is moving with velocity u and a source of sound moves with velocity 2

u in

u

u/2 S

the same direction as shown in the figure. Assuming that the sound travels with

velocity 10u. The ratio of incident sound wavelength on the wall to the

reflected sound wavelength by the wall, is equal to

(A) 9:11 (B) 11:9 (C) 4:5 (D) 5:4

24. S1 & S

2 are two coherent sources of sound having no initial phase difference. The

s2

s1

3m velocity of sound is 330 m/s. No minima will be formed on the line passing through

S2 and perpendicular to the line joining S

1 and S

2 , if the frequency of

both the sources is :

(A) 50 Hz (B) 60 Hz (C) 70 Hz (D) 80 Hz

MATRIX - MATCH TYPE

25. Match the column :

Column–I Column–II

(A) (P) Speed of component travelling wave is portion

Two strings each of length and linear mass AP will be

T

density and 9 are joined together and

system is oscillated such that joint P is node

T is tension in the strings. A and B are fixed ends.

(B) (Q) Speed of component travelling wave in the

Two strings each of length and linear mass portion AP will be more than that in portion BP.

density and 9 are joined together and

system is oscillated such that joint P is antinode.

T is tension in each string.A and B are fixed ends.

190


(C) (R) Frequency of oscillation of the system AB can

P is the mid–point of the string fixed at both ends. be

T

2

1

T is tension in the string and is its linear mass

density.

(D) (S) Frequency of oscillation of the system AB can

T is the tension in the string fixed at A and B is free be

T

4

1

end. P is mid–point. is its the linear mass density.

(T) Wavelength of the wave in the portion PB can

be 3

2.

26. Match the columns I & II.

Column I Column II

(A) Pitch (P) Number of harmonics present in the sound

(B) Loudness (Q) Intensity

(C) Quality (R) Frequency

(D) wave front (S) wave form

(T) locus of points vribrating in a phase

ASSERTION AND REASON TYPE

These questions contains, Statement 1 (assertion) and Statement II (reason).

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True.

27. Assertion : In a small segment of string carrying sinusoidal wave, total energy is conserved.

Reason : Every small part moves in SHM and in SHM total energy is conserved.

28. Assertion : Two waves moving in a uniform string having uniform tension cannot have different velocities.

Reason : Elastic and inertial properties of string are same for all waves in same string. Moreover speed of

wave in a string depends on its elastic and inertial properties only.

29. Assertion : Doppler formula for sound wave is symmetric with respect to the speed of source and speed of observer

Reason : Motion of source with respect to stationary observer is not equivalent to the motion of an observer with

respect to a stationary source.

30. Assertion : The base of Laplace correction was that exchange of heat between the region of compression andrarefaction in air is negligible.

Reason : Air is bad conductor of heat and velocity of sound in air is quite large.

WAVES

191

EXERCISE - 1

1. D 2. C 3. D 4. D 5. A 6. D 7. A 8. A 9. B 10. D 11. D 12. B 13. B

14. C 15. D 16. B 17. B 18. D 19. A 20. C 21. C 22. B 23. A 24. B 25. B 26. D

27. D 28. B 29. B 30. C 31. C 32. C 33. C 34. D 35. A 36. A 37. B 38. C 39. C

40. A 41. D 42. B 43. C 44. C 45. C 46. D 47. B 48. C 49. A 50. C 51. B 52. A

53. C 54. A 55. B

EXERCISE - 2

1. C 2. C 3. A 4. D 5. C 6. B 7. A 8. B 9. B 10. A 11. C 12. D 13. C

14. A 15. A 16. A 17. A 18. C 19. D 20. D 21. C 22. C 23. C 24. D 25. B 26. A

27. A 28. A 29. D 30. A 31. A 32. B 33. A 34. C 35. C 36. B 37. A 38. A 39. B

40. C 41. C 42. B 43. C 44. D 45. A 46. A 47. C 48. D 49. A 50. A 51. D 52. B

53. A

EXERCISE - 3 : PART # 1

1. A P, Q ; B S ; C P.R. ;D S 2. A Q ; B P ; C P 3. A Q ; B P ; C R

4. A Q ; B R ;C S ; D P 5. A R ; B P; C Q ; D T

PART # 2

1. A 2. B 3. D 4. E 5. A 6. E 7. C 8. A 9. E 10. C 11. B 12. E 13. A

14. C 15. A 16. D 17. B 18. B 19. A 20. D 21. C 22. A 23. C 24. A 25. B

EXERCISE - 4 : PART # 1

1. A 2. C 3. B 4. B 5. B 6. D 7. C 8. B 9. D 10. B 11. A 12. A 13. B

14. D 15. D 16. A 17. B 18. D 19. C 20. D 21. C 22. D 23. C 24. B 25. D 26. D

27. C 28. C 29. C 30. B 31. C 32. D 33. A 34. B 35. C 36. A 37. B 38. A 39. B

40. D 41. B

PART # 2

1. C 2. A 3. B 4. B 5. B 6. C 7. A 8. C 9. C 10. C 11. C 12. A 13. C

14. A 15. C 16. A 17. C 18. C 19. B 20. B 21. A 22. B 23. C 24. B 25. C 26. D

27. C 28. A 29. C 30. A 31. B 32. B 33. B 34. A 35. A

MOCK TEST

1. D 2. B 3. C 4. A 5. B 6. B 7. B 8. B 9. B 10. C 11. B 12. A 13. A

14. A 15. A 16. C 17. D 18. B 19. C 20. A 21. C 22. C 23. A 24. A

25. A P,Q,R,T ; B P,Q,S ; C P,R,S,T ; D P,S

26. A R ; B Q; C P,S ; D T 27. D 28. D 29. D 30. A

ANSWER KEY

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