Doppler Effect

5/22/2018 Doppler Effect

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Honorato C. Perez Sr. Memorial Science High School

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The oppler EffectJuly 6, 2009
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Doppler Effectphenomenon happened when a source of

sound and listener are in motion relative toeach other, the frequency of sound heard

by the listener is not the same as the

source frequency.first described by Christian Dopplerin the

19thcentury.



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Resting sound source

source

at rest

observer

at rest

Frequency fs Frequency foV=340m/s


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Stationary Source

Stationary Source

c = f

=c

f


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Moving ListenerA listener moving with a velocity vL toward astationary source S, the source S emits a sound

wave with frequency fs and wavelength, = v /fs. The wave crest approaching the moving listener

have a speed of propagation relative to the listener

of (v + vL) . So the frequency f

Lwith which the crest

arrive at the listenersposition is

fL = v + v L/ = v + vL / v / fS

fL= ( v + v L/ v) fS


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A listener toward a source ( vL> 0)hears a higher frequency than does astationary listener. A listener moving

away from the source ( vL< 0) hears alower frequency.


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observer

source observer

at rest

Frequency fsFrequency fo

o sf f

Observer hears

increased pitch

(shorter wave length)


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Sound source moving awayfrom observer

o sf f

sourceobserver

at rest

Frequency fsFrequency fo

Observer hears

decreased pitch(longer wave length)


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Moving Source and Moving Listener

= v / f SvS/ fS = v vS/ fS

( wavelength in front of moving source)

= v / fS+ vS/ f = v + v S / fS( wavelength behind a moving source)

In the region in front and behind the source wavelength are compressed and stretched out respectively, by the

motion of the source.


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To find the frequency heard by the listenerbehind the source:

fL= ( v + v L/ v + vS) fS

(Doppler effect, moving source and

moving listener)


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ConventionWe choose the positive direction (+)

for both vS and vL from the listener tothe source.

L SThe speed of sound v relative to the

medium is always positive.


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Sample Problem

1. A police siren emits a sinusoidal wave with

frequency fS = 300 Hz. The speed ofsound is 340 m/s. a) Find the wavelength

of the waves if the siren is at rest in the

air. b) if the siren is moving at 30 m/s, findthe wavelengths of the waves ahead and

behind the source.


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2. If a listener L is at rest and the

siren in ex.1 is moving away from L

at 30 m/s, what frequency doesthe listener hear?

3. If the siren is at rest and thelistener is moving toward left at 30

m/s, what frequency does the

listener hear?


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seatwork: An ambulance travelling at 18.0m/s emits

sound waves with frequency 400 Hz. The speed ofsound in air is 344m/s.

1. find the wavelength of the sound waves.

2.Calculate the frequency of the waves as

perceived by a man standing while the ambulanceis moving away from him. Make a sketch of thesituation

3. A girl standing at the side of street sees the

oncoming ambulance. What is the frequency of thesound waves as perceived by the girl?

What is the frequency perceived by a passenger in aca moving behind the ambulance in the same

direction but a speed of 15 m/s?

Doppler Effect

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