Doppler Effect t Harish

8/9/2019 Doppler Effect t Harish

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DOPPLEREFFECT


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ABSTR

ACT

In our everyday life, we are used to perceive soundby our sense of hearing. Sounds are the vibrations

that travel through the air. It is characterized by thewave quantities which include frequency, wavelength,period and speed.

The presentation aims to give basic concepts on

Doppler Effect in sound. It would help us understandthe changes in the relative motion of the source andthe observer.


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One might wonder why the siren on a

moving ambulance seems to produce sound

with a higher pitch when it passes anobserver and decreases when it recede the

observer.

Is this simply because of the relativedistance between the observer and the

ambulance (sound)?

Or is it because of the loudness of the sound

produced by the siren?


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This effect was named from the Austrianphysicist, Christian Johann Doppler, whofirst stated the physical principle in 1842.

Doppler Effect is the change in thefrequency (or wavelength) of any emittedwaves, such as a wave of light or sound asthe source of the wave approaches ormoves away from an observer.


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Dopplers principle explains why, if thesource of waves and the observer areapproaching each other, the sound heard bythe observer becomes higher in pitch,whereas if the source and observer are

moving apart the pitch becomes lower.

For the sound waves to propagate itrequires a medium such as air, where it

serves as a frame of reference with respectto which motion of source and observer aremeasured.


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SITUATION 1 STATIONARY SOURCE AND OBSERVERS

(NO DOPPLER EFFECT)

A stationary sound source S emits a spherical wavefronts of oneA stationary sound source S emits a spherical wavefronts of one apartapartspread out at speedspread out at speed vv relative to the medium air.relative to the medium air.

In timeIn time tt, the wavefronts move a distance, the wavefronts move a distance vtvt toward the observers, Otoward the observers, O11 &&OO2.2.

The number of wavelengths detected by the observer infront and behindThe number of wavelengths detected by the observer infront and behind

the source are the same and equal tothe source are the same and equal to vtvt//..


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What if both of the observers in figure 1 areWhat if both of the observers in figure 1 aremoving, is there any change in themoving, is there any change in the

frequency and wavelength of the source?frequency and wavelength of the source?


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SITUATION 2 STATIONARY SOURCE; MOVING

OBSERVERS

Observer 1 moves a distanceObserver 1 moves a distance vvoott toward the source at speedtoward the source at speed vvoo

We had known earlier that wavefronts also move at speedWe had known earlier that wavefronts also move at speed vvtowards Otowards O11 in time t at distancein time t at distance vtvt. The distance traveled by the. The distance traveled by thewavefronts with respect to Owavefronts with respect to O11 becomesbecomes vtvt ++ vvOOtt..

The number of wavelengths intercepted by OThe number of wavelengths intercepted by O11 at this distance isat this distance is((vt + v0tvt + v0t)/)/ ..


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From equation (1), we have = v/ f, fbecomes

(3)

This shows that there is an increase in the frequency fheard by O1 as it goes nearer to the sound source as

given by,

(2)


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If observer 2 moves away from the sound source, the distancetraveled by the wavefronts with respect to O2 in time t, is vt vot.

Consequently, there would be a decrease in the frequency heard by O2as given by,

(4)


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Combining Equations (3) and (4), we have

(5)

(STATIONARY SOURCE; MOVING OBSERVER)

In these situations only the frequency heard by theobservers changes due to there motion relative to thesource. However the wavelength of sound remains constant.


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SITUATION 3 MOVING SOURCE; STATIONARY

OBSERVERS

As the source moves a distance vST (T=1/f period of wave) toward O1there is a decrease in the wavelength of sound by a quantity of vsT. The shortened wavelength becomes

= vsT


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The frequencyThe frequency ffof sound wave heard by Oof sound wave heard by O11 increasesincreases

as given by,as given by,

(6)


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With respect to observer 2, the wavelength of sound increases,where becomes + vsT.

The frequency f of sound wave heard by O2 decreases as givenby,

(7)


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Combining Equations (6) and (7), we have

(8)

(MOVING SOURCE; STATIONARY OBSERVER)


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SITUATION 4 Moving Source and

Observer

From the equations (5) and (8), we can now derive theequation of general Doppler Effect by replacing f inequation (5) with f of equation (8). This result to,

(MOVING SOURCE AND OBSERVER)

(9)


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(9)

The signs correspond to the direction of the source orobserver when they are moving relative to the other. Thesewould determine whether there is an increase or decreaseon the frequency heard by the observer during the motion.


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(APPROACHING OBSERVER; RECEEDING SOURCE)(APPROACHING OBSERVER; RECEEDING SOURCE)

If vIf voo> v> vss , increase in observed frequency, increase in observed frequency

If vIf voo< v< vss , decrease in observed frequency, decrease in observed frequency

(RECEEDING OBSERVER; RECEEDING SOURCE)(RECEEDING OBSERVER; RECEEDING SOURCE)

Decrease in observed frequencyDecrease in observed frequency


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(APPROACHING OBSERVER; APPROACHING SOURCE)(APPROACHING OBSERVER; APPROACHING SOURCE)

Increase in observed frequencyIncrease in observed frequency

(RECEEDING(RECEEDING OBSERVER; APPROACHING SOURCE)OBSERVER; APPROACHING SOURCE)

If vIf voo> v> vss , decrease in observed frequency, decrease in observed frequency

If vIf voo< v< vss , increase in observed frequency, increase in observed frequency


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APPLICATIONSOF DOPPLER EFFECT (RADARSPEED TRAP)

The police monitor the speeds of vehicles withThe police monitor the speeds of vehicles with

radar gun. The radar gun send microwavesradar gun. The radar gun send microwavestowards the car. The wave reflected back totowards the car. The wave reflected back tothe gun have a higher frequency because ofthe gun have a higher frequency because ofthe Doppler effect.the Doppler effect.

The microwave receiver inThe microwave receiver inthe radar gun detects thethe radar gun detects thedifference in frequencydifference in frequency ((ffbetween the emitted signalbetween the emitted signal

and the received signal.and the received signal.The speed of the car isThe speed of the car iscalculated from this, andcalculated from this, anddisplayed automaticallydisplayed automatically

on a screen.on a screen.


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WEATHER RADAR

Both humidity (reflected intensity) and speed of cloudsBoth humidity (reflected intensity) and speed of clouds(doppler effect) are measured.(doppler effect) are measured.


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Ultrasonic waves reflected from red blood cellsUltrasonic waves reflected from red blood cellscan be used to determine the velocity of blood flow.can be used to determine the velocity of blood flow.

APPLICATIONSOF DOPPLER EFFECT (MEDICINE)


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Reflection of ultrasonic waves can also be used toReflection of ultrasonic waves can also be used to

detect the movement of the chest of a youngdetect the movement of the chest of a youngfetus and to monitor its heartbeat.fetus and to monitor its heartbeat.


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Thats all folks!Thats all folks!

Doppler Effect t Harish

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