Physics 201Professor P. Q. Hung

311B, Physics Building

Physics 201 – p. 1/21

Waves and Sound

Types of waves

Mechanical waves: waves that exist onlywithin a material medium such as water, airand rock for example. Examples: waterwaves, sound waves and seismic waves.

Transverse Waves: displacement of particlesperpendicular to the direction of wavepropagation, e.g. wave propagating along astring.

Longitudinal Waves: displacement ofparticles along the direction on wavepropagation, e.g. sound waves.

Physics 201 – p. 2/21

Waves and Sound

Types of waves

Mechanical waves: waves that exist onlywithin a material medium such as water, airand rock for example. Examples: waterwaves, sound waves and seismic waves.

Transverse Waves: displacement of particlesperpendicular to the direction of wavepropagation, e.g. wave propagating along astring.

Longitudinal Waves: displacement ofparticles along the direction on wavepropagation, e.g. sound waves.

Physics 201 – p. 2/21

Waves and Sound

Types of waves

Mechanical waves: waves that exist onlywithin a material medium such as water, airand rock for example. Examples: waterwaves, sound waves and seismic waves.

Transverse Waves: displacement of particlesperpendicular to the direction of wavepropagation, e.g. wave propagating along astring.

Longitudinal Waves: displacement ofparticles along the direction on wavepropagation, e.g. sound waves. Physics 201 – p. 2/21

Waves and Sound

Transverse waves

Physics 201 – p. 3/21

Waves and Sound

Transverse waves

Physics 201 – p. 4/21

Waves and Sound

Longitudinal waves

Physics 201 – p. 5/21

Waves and Sound

Water waves

Physics 201 – p. 6/21

Waves and Sound

Water waves

Water wave: Combination of Transverse andLongitudinal motion.

Physics 201 – p. 7/21

Waves and Sound

Characteristic of a wave

Amplitude A: magnitude of the maximumdisplacement of the particles from theirequilibrium positions as the wave passesthrough them.

Wavelength: distance (parallel to the directionof wave propagation) between repetitions ofthe shape of the wave. Denoted by λ

Period: time required for one wavelength topass a given point. Denoted by T .

Physics 201 – p. 8/21

Waves and Sound

Characteristic of a wave

Amplitude A: magnitude of the maximumdisplacement of the particles from theirequilibrium positions as the wave passesthrough them.

Wavelength: distance (parallel to the directionof wave propagation) between repetitions ofthe shape of the wave. Denoted by λ

Period: time required for one wavelength topass a given point. Denoted by T .

Physics 201 – p. 8/21

Waves and Sound

Characteristic of a wave

Amplitude A: magnitude of the maximumdisplacement of the particles from theirequilibrium positions as the wave passesthrough them.

Wavelength: distance (parallel to the directionof wave propagation) between repetitions ofthe shape of the wave. Denoted by λ

Period: time required for one wavelength topass a given point. Denoted by T .

Physics 201 – p. 8/21

Waves and Sound

Characteristic of a wave

Frequency: f = 1/T .

Angular frequency: ω = 2πf

Wave speed: v = λT = λf .

Wave number: k = 2πλ .

Physics 201 – p. 9/21

Waves and Sound

Characteristic of a wave

Frequency: f = 1/T .

Angular frequency: ω = 2πf

Wave speed: v = λT = λf .

Wave number: k = 2πλ .

Physics 201 – p. 9/21

Waves and Sound

Characteristic of a wave

Frequency: f = 1/T .

Angular frequency: ω = 2πf

Wave speed: v = λT = λf .

Wave number: k = 2πλ .

Physics 201 – p. 9/21

Waves and Sound

Characteristic of a wave

Frequency: f = 1/T .

Angular frequency: ω = 2πf

Wave speed: v = λT = λf .

Wave number: k = 2πλ .

Physics 201 – p. 9/21

Waves and Sound

Simple ExampleA sinusoidal wave travels along a string. Thetime for a particular point to move from maximumdisplacement to zero is 0.170s. What are (a) theperiod and (b) the frequency? (c) Thewavelength is 1.40m; what is the wave speed?

Maximum to zero: one quater of the period ⇒

T = 4 × 0.170s = 0.680 s.

Frequency: f = 1T = 1.47Hz.

Wave speed: v = λT = 2.06 m/s.

Physics 201 – p. 10/21

Waves and Sound

Simple ExampleA sinusoidal wave travels along a string. Thetime for a particular point to move from maximumdisplacement to zero is 0.170s. What are (a) theperiod and (b) the frequency? (c) Thewavelength is 1.40m; what is the wave speed?

Maximum to zero: one quater of the period ⇒

T = 4 × 0.170s = 0.680 s.

Frequency: f = 1T = 1.47Hz.

Wave speed: v = λT = 2.06 m/s.

Physics 201 – p. 10/21

Waves and Sound

Simple ExampleA sinusoidal wave travels along a string. Thetime for a particular point to move from maximumdisplacement to zero is 0.170s. What are (a) theperiod and (b) the frequency? (c) Thewavelength is 1.40m; what is the wave speed?

Maximum to zero: one quater of the period ⇒

T = 4 × 0.170s = 0.680 s.

Frequency: f = 1T = 1.47Hz.

Wave speed: v = λT = 2.06 m/s.

Physics 201 – p. 10/21

Waves and Sound

Waves on a stretched stringThe wave speed on a stretched string dependsonly on the tension and the linear density of thestring. If the mass of the string is m and its lengthis L, one has

v =√

Fµ . F : Tension

µ = m/L: Linear density.

Physics 201 – p. 11/21

Waves and Sound

Waves on a stretched stringThe wave speed on a stretched string dependsonly on the tension and the linear density of thestring. If the mass of the string is m and its lengthis L, one has

v =√

Fµ . F : Tension

µ = m/L: Linear density.

Physics 201 – p. 11/21

Waves and Sound

Waves on a stretched stringTwo strings are tied together with a knot and thenstretched between two rigid supports. Thestrings have linear densities µ1 = 1.4 × 10−4kg/mand µ2 = 2.8 × 10−4kg/m. Their lengths areL1 = 3.0m and L2 = 2.0m and string 1 is under atension of 400N . Simultaneously, on each stringa pulse is sent from the rigid support end, towardthe knot. Which pulse reaches the knot first?

Concept: Since the strings a tied together bya knot, they both have the same tension.

Physics 201 – p. 12/21

Waves and Sound

Waves on a stretched string

For string 1, the time ist1 = L1

v1

= L1

√

µ1

F = 1.77 × 10−3 s

Similarly, for string 2, one hast2 = L2

v2

= L2

√

µ2

F = 1.67 × 10−3 s. So the pulseon string 2 reaches the knot first..

Physics 201 – p. 13/21

Waves and Sound

Waves on a stretched string

For string 1, the time ist1 = L1

v1

= L1

√

µ1

F = 1.77 × 10−3 s

Similarly, for string 2, one hast2 = L2

v2

= L2

√

µ2

F = 1.67 × 10−3 s. So the pulseon string 2 reaches the knot first..

Physics 201 – p. 13/21

Waves and Sound

Reflections

Physics 201 – p. 14/21

Waves and Sound

Harmonic Waves

A transverse wave on a string traveling to theright can be described by a functiony(x, t) = A cos(kx − ωt)where k and ω are defined above.

For a wave traveling to the left, one wouldhavey(x, t) = A cos(kx + ωt)

Physics 201 – p. 15/21

Waves and Sound

Harmonic Waves

A transverse wave on a string traveling to theright can be described by a functiony(x, t) = A cos(kx − ωt)where k and ω are defined above.

For a wave traveling to the left, one wouldhavey(x, t) = A cos(kx + ωt)

Physics 201 – p. 15/21

Waves and Sound

Sound Waves

Sound waves are longitudinal waves whicharises when the medium, e.g. air, isalternately compressed and rarified. Thespeed of sound in the medium depends onquantities such as the density, etc..

The speed of sound in air at normal pressureand temperature (1 atm at 200C isv = 343 m/s

Physics 201 – p. 16/21

Waves and Sound

Sound Waves

Sound waves are longitudinal waves whicharises when the medium, e.g. air, isalternately compressed and rarified. Thespeed of sound in the medium depends onquantities such as the density, etc..

The speed of sound in air at normal pressureand temperature (1 atm at 200C isv = 343 m/s

Physics 201 – p. 16/21

Waves and Sound

Sound Waves

Frequency ⇒ Pitch. Normal hearing:20Hz − 20, 000Hz. Ultrasound:f > 20, 000Hz. Infrasound: f < 20Hz. Manyphenomena and applications.

v = λf

Physics 201 – p. 17/21

Waves and Sound

Sound Waves

Frequency ⇒ Pitch. Normal hearing:20Hz − 20, 000Hz. Ultrasound:f > 20, 000Hz. Infrasound: f < 20Hz. Manyphenomena and applications.

v = λf

Physics 201 – p. 17/21

Waves and Sound

Sound Waves

Physics 201 – p. 18/21

Waves and Sound

Sound Waves

Physics 201 – p. 19/21

Waves and Sound

Sound WavesTo understand the numbers in the previous table:

Speed of sound in long solid rod: v =√

Eρ . E:

Young modulus related the stretch of a solid.ρ: density of the material. E.g. Iron:E = 1011 N/m2, ρ = 7.8 × 103 kg/m3.

Speed of sound in liquid or gas: v =√

Bρ . B:

Bulk modulus related the compression. E.g.Air: B = 1.01 × 105 N/m2, ρ = 1.29 kg/m3

Physics 201 – p. 20/21

Waves and Sound

Sound WavesTo understand the numbers in the previous table:

Speed of sound in long solid rod: v =√

Eρ . E:

Young modulus related the stretch of a solid.ρ: density of the material. E.g. Iron:E = 1011 N/m2, ρ = 7.8 × 103 kg/m3.

Speed of sound in liquid or gas: v =√

Bρ . B:

Bulk modulus related the compression. E.g.Air: B = 1.01 × 105 N/m2, ρ = 1.29 kg/m3

Physics 201 – p. 20/21

Waves and Sound

Sound Waves(a) Estimate the wavelength of a sea animal’secholocation wave if the frequency is 100, 000 Hz;(b) If an obstacle is 100 m from the animal, howlong after the animal emits a wave is its relectiondetected?

v =√

Bρ =

√

2.0×109N/m2

1.025×103kg/m3 = 1.4 × 103 m/s ⇒

λ = vf = 1.4×103 m/s

1.0×105Hz = 14mm

t = 2(100m)1.4×103 m/s = 0.14s

Physics 201 – p. 21/21

Waves and Sound

Sound Waves(a) Estimate the wavelength of a sea animal’secholocation wave if the frequency is 100, 000 Hz;(b) If an obstacle is 100 m from the animal, howlong after the animal emits a wave is its relectiondetected?

v =√

Bρ =

√

2.0×109N/m2

1.025×103kg/m3 = 1.4 × 103 m/s ⇒

λ = vf = 1.4×103 m/s

1.0×105Hz = 14mm

t = 2(100m)1.4×103 m/s = 0.14s

Physics 201 – p. 21/21