Chapter 12

SOUND

SOUND

SOUND• Sound Waves are longitudinal waves: The

particles of the medium through which it propagates oscillates in the same direction along which the waves travel.

• Vibrating objects produce sound: guitar strings, speakers etc.

• Speaker cones produce pressure variations by displacing air molecules from a uniform distribution.

• Rarefactions (relaxed) and compression regions are formed.

Sound Wave Generated by a Loudspeaker

Frequency Ranges• Velocity of wave: v = f.

• The human ear can respond to only a limited range of sound frequency – called the audible range: 20 Hz to 20 kHz.

• Ultrasound – beyond 20 kHz, Infrasound – below 20 Hz.

• Animals can detect sound beyond the audible range: Dolphins can pick sound at 250 kHz. Dogs can pick sound at 50 kHz. Elephants communicate using sound waves at 10 Hz.

Frequency Ranges• The speed of sound differs in different media.

• Also speed depends on temperature (v T)

Medium Speed (m/s)

Air 331

Carbon dioxide CO2 259

Hydrogen (H2) 1,284

Mercury (25oC) 1,450

Water (25oC) 1,493

Concrete 3,100

Granite 6,500

Loudness• Loudness of sound is related to amplitude of

the sound wave – maximum displacement of the medium particles.

• All things being equal, larger amplitude means louder sound.

• Intensity (I) of sound is defined as the average power of the wave per unit area.

• I = power/area = P/4r2

• SI unit of intensity is watts/m2 (W/m2).

• The wave traveling in all directions.

Loudness• Intensity (amplitude)2.

• Louder sound has larger amplitude or larger intensity.

Example

• If at 30 m, the intensity of a sound is 100 W/m2, what will the intensity be at 300 m away?

I 1/r2 OR I1r12 = I2r2

2

I2 = (I1r12)/r2

2

I2 = (100 x 30 x 30)/3002 = 1 W/m2

Intensity

• Louder sound has larger amplitude or larger intensity.

• Perception of loudness by the human ear varies logarithmically with intensity of sound ie, Loudness Log of Intensity.

• The lowest intensity of sound that can be detected by the human ear is called the threshold of hearing and is equal to

Io = 10-12 W/m2.

Decibels

• Sound intensity level () in units of decibels (dB) is defined as the log10 of the ratio of a sound intensity to the threshold intensity, Io.

= (10dB)log10(I/Io).

• 0 dB = threshold of hearing.

• If a sound has intensity of 10-5 W/m2, its intensity level is

= 10dBlog10(10-5/10-12)

= 10log10(107) = 10 x 7 = 70 dB.

Logarithms

• Log101 = Log10100 = 0

• Log1010 = Log10101 = 1

• Log10100 = Log10102 = 2

• Log10(a/b) = Log10(a) – Log10(b)

• Log10(ab) = Log10(a) + Log10(b)

Example

• If at 30 m, the intensity of a sound is 100 W/m2, what is the sound intensity level at this distance?

= (10dB)log10(I/Io).

= (10dB)log10(102/10-12).

= (10dB)log10(1014).

= 140 dB

Decibels

• If 1 person can shout with loudness 50 dB. How loud will it be when 100 people shout?

1) 52 dB 2) 70 dB 3) 150 dB

1 = (10 dB) log10(I1/I0)

100 = (10 dB) log10(I100/I0)

100 – 1 = (10 dB) log10(I100/I1)

100 = 50 + (10 dB) log10(100/1)

100 = 50 + 20

Intensity

• Recall Intensity = P/A. If you are standing 6 meters from a speaker, and you walk towards it until you are 3 meters away, by what factor has the intensity of the sound increased?

1) 2 2) 4 3) 8

Area goes as d2 so if you are ½ the distance the intensity will increase by a factor of 4

Suppose you are standing a distance D away from a speaker that is radiating sound in a spherically uniform way. You walk away from the speaker until the loudness of the sound is reduced by a factor of two. About how far from the speaker are you now? (neglect any reflections from the ground)

1. 10D

2. 4D

3. 3D

4. 2D

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 1.5 s after shouting. Estimate the length of the lake. [Use v = 330 m/s]

What is the intensity of sound at the pain level of 120 dB?

Compare it to that of a whisper at 46 dB.

Human beings can typically detect a difference in sound intensity level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?

Examples

Noise produced by an engine has a sound level of 200 dB when measured at 50 m from the source. At this location, what is the intensity of this noise?

(A) 108 W/m2 (B) 10-10 W/m2 (C)

14.3 W/m2

(D) 10-8 W/m2 (E) 143 W/m2

Examples

Which of the following statements is correct? (A)   Sound is an example of transverse waves. (B)    The threshold of hearing is the lowest frequency a normal human ear can detect.(C)   At the threshold of hearing, the sound intensity level is 0 dB.(D)   The audible range is a range of intensities a normal human ear can detect.(E)    The intensity of sound will increase if you increase your distance from the source of the sound.

The intensity of a sound 20 m away from the source is 85.0 W/m2. What is the sound intensity level, , at this distance?

 (A) 320.7 dB (B) 100.1 dB (C) 13.93 dB (D) 139.3 dB (E) 1,393 dB

Examples

If the intensity of a sound source is doubled, by how much will the sound intensity level increase?

If the intensity of a sound source is doubled, the sound intensity level will increase by 3 dB.

Adding 3 dB to a sound intensity level doubles its intensity.

If the intensity of a sound source is increased by a factor of ten, by how much will the sound intensity level increase?

If the intensity of a sound source is increased by a factor of 10, the sound intensity level will increase by 10 dB.

Adding 10 dB to a sound intensity level raises its intensity ten times.

An unfingered guitar string is 0.70 m long an is tuned to play E above middle C (330 Hz). How far from the end of this string much the finger be placed to play A above middle C (440 Hz)?

• Pitch of sound (high or low) corresponds to frequency.

• High pitch = high frequency.

• Low pitch = low frequency.

Pitch log10(f), i.e. pitch is a logarithmic function of frequency.

A sound wave having frequency f0, speed v0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is 1 Compare the frequency of the sound wave inside and outside the balloon

1. f1 < f0

2. f1 = f0

3. f1 > f0f1

f0

A sound wave having frequency f0, speed v0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is 1.

Compare the speed of the sound wave inside and outside the balloon.

1. v1 < v0

2. v1 = v0

3. v1 > v0 V1=965m/sV0=343m/s

A sound wave having frequency f0, speed v0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f1, its speed is v1, and its wavelength is 1 Compare the wavelength of the sound wave inside and outside the balloon

1. 1 < 0

2. 1 = 0

3. 1 > 0

0 1

= v / f

Standing Waves• Recall for string

– Node at each end – Standing wave n = 2L/n – or fn = n v/(2L) = nf1

Standing Waves

For Pipe open at both ends

– Pressure node at each end

– Standing wave n = 2L/n or fn = n v/(2L)

• For Pipe open at one end, pressure node at one end anti node at other.– Standing wave n = 4L/n or fn = n

v/(4L) n =1, 3, 5.. Or fn = nf1

Resonance

• What happens to the fundamental frequency of a pipe, if the air (v=300 m/s) is replaced by helium (v=900 m/s)?

1) Increases 2) Same 3) Decreases

f = v/(4L)

THE END

Intensity and Loudness• Intensity if the power per unit area.

–I = P / A–Units Watts/m2

• For Sound Waves–I = p0

2 / (2 v)–Proportional to p0

2 note Energy goes as A2

• Loudness (Decibels)–Loudness perception is logarithmic–Threshold for hearing I0 = 10-12 W/m2

= (10 dB) log10 ( I / I0) 2 – 1 = (10 dB) log10(I2/I1)

Speaker radiating power P

I1 = P/(4D12)

D1

I2 = P/(4D22)

D2

Changing I by 10 will changeloudness by 2 (pg 412 in text)

We want I1/I2 = 10

21

22

22

212

1

44 D

D

D

P

D

PII

10

21

22 D

D

112 16.310 DDD

Preflight 5• As a police car passes you with its siren

on, the frequency of the sound you hear from its siren

1) Increases 2) Decreases 3) Same

Doppler Example Audio

Doppler Example Visual

Doppler Effect moving source

• When source is coming toward you– Distance between waves decreases

– Frequency increases

• When source is going away from you– Distance between waves increases

– Frequency decreases

• fo = fs / (1- vs/v)

Doppler Effect moving observer• When moving toward source

– Distance between waves decreases

– Frequency increases

• When away from source– Distance between waves increases

– Frequency decreases

• fo = fs (1- vo/v)

Combine: fo = fs (1-vo/v) / (1-vs/v)

DopplerA: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on.

B: You and the police car have both pulled over to the side of the road, but the siren is still turned on.

In which case does the frequency of the siren seem higher to you?

1. Case A

2. Case B

3. same

v

vv

v

ff

s

o

1

1'

vs

f

vo

f’v

correct

Pg 427