MSU Physics 231 Fall 2015 1 Physics 231 Topic 11: Waves & Sound Alex Brown Nov 11-16 2015

LE 01-10b

Physics 231

Topic 11: Waves & Sound

Alex Brown

Nov 11-16 2015

MSU Physics 231 Fall 2015

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Key Concepts: Waves & Sound

Wave Properties

Transverse vs longitudinal waves

Wave periodicity a speed

Interference and Standing Waves

Superposition, constructive & destructive interference

Sound Waves

Sound Intensity

Musical Instruments & Harmony

The Doppler Effect

Covers chapter 11 in Rex & Wolfson


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The wave moves to the right, but each point makes a

simple harmonic vertical motion

Since the oscillation is in the direction perpendicular (transverse) to the direction of travel, this is called a transverse wave. Example: water waves

position x

position y

Wave motion

oscillation

Transverse Waves


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3

Describing a Traveling Wave

While the wave has traveled one wavelength, each point on the wave

has made one period of oscillation.

v = x/t = /T = f

: wavelength = length (m) of one oscillation.

T: period = time for one oscillation

T=1/f f: frequency (Hz)

x

y

t=0

t=T/4

t=2T/4

t=3T/4

t=T


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An Example

A traveling transverse wave is seen to have horizontal distance of 2m between a maximum and the nearest minimum and a peak maximum to peak minimum height of 3m. If it moves at 1m/s, what is its:

amplitude

period

frequency

amplitude: difference between maximum (or minimum)

and the equilibrium position in the vertical direction

(transversal!) A = 1.5m

v = 1m/s, =2*2m = 4m T = /v = 4/1 = 4s

f = 1/T = 0.25 Hz


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Quiz

Two speakers sitting next to each other emit sound waves at two different frequencies. The first emits a sound wave with a frequency of 1 kHz and a wavelength of 0.3m. The second sound wave emits a sound wave at 100 Hz with a wavelength of 3m. If started at the same time, which sound wave reaches your ears first?

The first sound wave

The second sound wave

They arrive at the same time

1 = 0.3m f1 = 1000Hz

2 = 3mf2 = 100Hz

v1 = 1 f1 = 0.31000 = 300 m/s

v2 = 2 f2 = 3100 = 300 m/s


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7

Sea Waves

An anchored fishing boat is going up and down with the

waves. It reaches a maximum height every 5 seconds

and a person on the boat sees that while reaching a

maximum, the previous wave has moved about 40 m away

from the boat. What is the speed of the traveling waves?

Period: 5 seconds (time between reaching two maxima)

Wavelength: 40 m

v = /T = 40/5 = 8 m/s


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Longitudinal Waves

Longitudinal wave: movement is in the direction of the

wave motion. Example: sound waves

oscillation

The wave moves to the right, but each point makes a simple harmonic horizontal motion

wave


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Sound: longitudinal waves

A sound wave consist of longitudinal oscillations in the

pressure of the medium that carries the sound wave.

Therefore, in vacuum: there is no sound.


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Relation between amplitude and intensity

time (s)

A

-A

x

For sound, the intensity I is proportional to the square of the amplitude of the longitudinal wave

I~A2


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Intensity

Intensity: rate of energy flow through an area

Power (P) J/s

A (m2)

Intensity: I = P/A (J/m2s = W/m2)

Even if you have a powerful sound source (say a speaker),

the intensity will be small when far away.


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Intensity and Distance

Sound from a point source produces a spherical wave.

Why does the sound get fainter further away from the source?


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Intensity and Distance

The amount of energy passing

through a spherical surface

at distance r from the source

is constant, but the surface

becomes larger.

I = Power/Surface = P/A = P/(4r2)

r=1 I = P/(4r2) = P/(4)1

r=2 I = P/(4r2) = P/(16)1/4

r=3 I = P/(4r2) = P/(36)1/9

I r2 = constant or I1/I2 = r22/r12


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Wave fronts

spherical waves

plane waves

Sound emitted from a

point source are

spherical. Far away

from that source, the

wave are nearly

plane.


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The Speed of Sound

Depends on the how easily the material is compressed (elastic property) and how much the material resists acceleration (inertial property)

v=(elastic property/inertial property)

v=(B/) B: bulk modulus : density

The velocity also depends on temperature.

In air: v=331(T/273 K)

so v=343 m/s at room temperature

The speed does not depend on the frequency

- how to we know this?


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Quiz

As you move farther from a source of light, the intensity

of the light

remains the same.

becomes smaller.

becomes larger.

The amount of energy passing

through a spherical surface

at distance r from the source

is constant, but the surface

becomes larger.

I = Power/Surface = P/A= P/(4r2)

Units = Watts/m2


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Intensity

Faintest sound we can hear:I~1x10-12 W/m2 (@ 1000 Hz)

Loudest sound we can stand:I~1 W/m2 (@ 1000 Hz)

Factor of 1012? Loudness works logarithmic

sound wave

vibrating

ear drum


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PHY 231

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Sound - Decibel Level

=10log (I/I0) I0=10-12 W/m2

y = log10x = log(x) inverse of x = 10y

( not this: y=ln(x) x=ey )

log(ab)= log(a) + log(b)

log(a/b)= log(a) - log(b)

log(an)= n log(a)


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Decibels (units are called dB)

For an increase of n dB:

the intensity of the sound is

multiplied by a factor of ?.

n = 2-1= 10 log(I2/I0) 10 log(I1/I0)

n = 10 log(I2/I1)

(n/10) = log(I2/I1) n (I2/I1)

10 10

10 (n/10) = (I2/I1) 20 100

30 1000

=10 log(I/I0) I0=10-12 W/m2


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Table of sound levels L and correspondingsound pressure and sound intensitySound SourcesExamples with distanceSound PressureLevel Lp dBSPLSound Pressure pN/m2 = PaSound Intensity IW/m2Jet aircraft, 50 m away 140200100Threshold of pain13063.210Threshold of discomfort 120201Chainsaw, 1 m distance 1106.310-1 0.1Disco, 1 m from speaker 100210-2 0.01Diesel truck, 10 m away900.6310-3 0.001Kerbside of busy road, 5 m 800.210-4 0.0001Vacuum cleaner, distance 1 m 700.06310-5 0.00001Conversational speech, 1 m 600.0210-6 0.000001Average home 500.006310-7 0.0000001Quiet library 400.00210-8 0.00000001Quiet bedroom at night300.0006310-9 0.000000001Background in TV studio200.000210-10 0.0000000001Rustling leaves in the distance100.00006310-1 1 0.00000000001Threshold of hearing00.0000210-1 2 0.000000000001
Sound Levels


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Example

A person living on campus (c) 300 m from the rail track

is tired of the noise of the passing trains. They decide to

move to Abbott (a) (3.5 km from the rail track). If the

Sound level of the trains was originally 70dB

(vacuum cleaner), what is the sound level at Abbott?

Campus (c): c = 70 dB = 10log (Ic/I0)

Ic= 107 I0 = 10-5 W/m2

Ia/Ic = rc2/ra2 = 0.0073

Ia = Ic (rc2/ra2) = 7.3x10-8 W/m2

Sound level: a = 49 dB (normal conversation)


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example

A machine produces sound with a level of 80dB. How

many machines can you add before exceeding 100dB?

1 machine

80 dB=10log(I/I0)

8=log(I/I0)=log(I/1E-12)

108=I/1E-12

I1=10-4 W/m2

N machines

100 dB=10log(I/I0)

10 = log(I/I0)=log(I/1E-12)

1010 = I/1E-12

IN=10-2 W/m2

I1/IN = 10-4/10-2 = 1/100

The intensity must increase by a factor of 100;

one needs to add 99 machines.

Shortcut: x = 20 so the increase in I is 10(x/10) = 100.


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Clicker Quiz

The speed of sound in a material does NOT depend on:

The density of the material

The frequency of the sound

The temperature of the material

The pressure on the material

None of the above

The speed of sound depends on the density of the material: higher density leads to lower sound speed!

The density and rigidity depend on the temperature of and the pressure on the material.

Higher frequency means lower wavelength (and vice versa). These properties are determined by the speed of sound in the material.


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24

question

An ambulance is moving towards you with its sirens on. The

pitch of the sound you hear is .......... than the pitch

you would hear if the ambulance were not moving at all.

higher

the same

lower


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Doppler effect: a non-moving source

source

you

vsound

f = vsound/


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doppler effect: a source moving towards you

source

observer

the distance between

the wave front is

shortened

The frequency becomes larger: higher tone

vsource

Prime (): heard observable


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Doppler Effect: a source moving away from you

source

observer

the distance between

the wave front becomes longer

The frequency becomes lower: lower tone

vsource


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Doppler Effect: you moving towards the source

source

observer

vsound

If you move away from source use vo < 0

Equivalent to increasing the velocity


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Doppler Effect: In General

source

you

vo =vobserver: positive if moving towards to source

vs = vsource: positive if moving towards the observer


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question

An ambulance is moving towards you with its sirens on. The

frequency of the sound you hear is than the frequency

you would hear if the ambulance were not moving at all.

higher

the same

lower


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applications of doppler effect: weather radar (radio waves electromagnetic)

Both humidity (reflected intensity) and speed of clouds

(doppler effect) are measured.


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example

A police car using its siren (frequency 1200Hz) is driving

west towards you over Grand River with a velocity of 25m/s.

You are driving east over grand river, also with 25m/s.

a) What is the frequency of the sound from the siren that

you hear? b) What would happen if you were also driving west

(behind the ambulance)? v = vsound = 343 m/s

a)

b)


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Interference: two wave same frequency

Constructive interference: maxima line up. Waves are in phase

Destructive interference:

maxima lines up with minimum.

Waves are out of phase by

Time (t)


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Interference

Two traveling pulse waves pass through each other without affecting each other. The resulting displacement is the superposition of the two individual waves.


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Interference: two different frequencies (beats)

Amplitude of the beat changes with time, so the intensity of the sound changes as a function of time. fbeat = |fA-fB|


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An Example: two speakers

Two speakers are placed 10m apart, facing each other. Each speaker is playing a pure tone (ie, 1 frequency) with the same amplitude. A student notices that the first speaker is making a tone of 340 Hz and that at 6m from this speaker, there is a minimum in sound intensity. What are the possible frequencies for the second speaker? (vsound = 340 m/s)


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Interference: Standing Wave

If two waves travel in opposite directions and v1=v2, the superposition of the two waves produces a standing wave:

maxima and minima always appear at the same location


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String: standing Wave

A string fixed at two ends can support different constructive resonances.

Requires that there is constructive interference: path length difference between NODES must be .

Node = point in the resonance with zero amplitude.


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40

Tube: standing Wave


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Standing Wave

Just like with sound, the velocity of the standing wave depends on the density of the material.

Linear mass density of a string:

= mass/length

Also depends on the strings tension: T

Power transmitted

by a wave on a string


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42

A 1-m-long piano wire has a mass of 1 gram and is under a tension of 160 N.

Find the wave speed for this string.

(b) If you want to tune this wire to make middle C (f = 256 Hz) the fundamental frequency, what should the wire tension be?

An Example


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Rubens tube with propane gas in a tube with a length of L=2.1 m

Resonance frequencies are observed at 742 and 680 Hz

Find the speed of sound in propane and the first harmonic frequency.

From the equation below v = 2L*62 = 260 m/s and f1 = 62 Hz


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Documents

MSU Physics 231 Fall 2015 1 Physics 231 Topic 11: Waves & Sound Alex Brown Nov 11-16 2015