Doppler Doppler EffectEffect

Angelourd T.Quibuyen and Ariel C. Angelourd T.Quibuyen and Ariel C. AlvarezAlvarez

Physics Department, Western Physics Department, Western Mindanao State UniversityMindanao State UniversityNormal Road, Baliwasan,Normal Road, Baliwasan, Zamboanga City 7000Zamboanga City 7000

AbstractAbstractIn our everyday life, we are used to perceive sound by our sense of hearing. Sounds are the vibrations that travel through the air. It is characterized by the wave quantities which include frequency, wavelength, period and speed.The paper aims to present basic concepts on Doppler Effect in sound. It would help us understand the changes in the relative motion of the source and the observer.

• One might wonder why the siren on a moving ambulance seems to produce sound with a higher pitch when it passes an observer and decreases when it recede the observer.

• Is this simply because of the relative distance between the observer and the ambulance (sound)?

• Or is it because of the loudness of the sound produced by the siren?

• This effect was named from the Austrian physicist, Christian Johann Doppler, who first stated the physical principle in 1842.

• Doppler Effect is the change in the frequency (or wavelength) of any emitted waves, such as a wave of light or sound as the source of the wave approaches or moves away from an observer.

• Doppler’s principle explains why, if the source of waves and the observer are approaching each other, the sound heard by the observer becomes higher in pitch, whereas if the source and observer are moving apart the pitch becomes lower. • For the sound waves to propagate it requires a medium such as air, where it serves as a frame of reference with respect to which motion of source and observer are measured.

SITUATION SITUATION 11 Stationary Source and Observers Stationary Source and Observers (NO DOPPLER EFFECT)(NO DOPPLER EFFECT)

• A stationary sound source S emits a spherical wavefronts of one A stationary sound source S emits a spherical wavefronts of one λ apart spread out at speed λ apart spread out at speed vv relative to the medium air. relative to the medium air.• In time In time tt, the wavefronts move a distance , the wavefronts move a distance vtvt toward the toward the observers, Oobservers, O11 & O & O2.2.

•The number of wavelengths detected by the observer infront The number of wavelengths detected by the observer infront and behind the source are the same and equal to and behind the source are the same and equal to vtvt/λ. /λ.

f - frequency of sound sourcev - speed of sound wavest - timeλ - wavelength

Thus, the frequency Thus, the frequency f f heard by both stationary heard by both stationary observers is given by,observers is given by,

What if both of the observers in figure What if both of the observers in figure 1 are moving, is there any change in 1 are moving, is there any change in the frequency and wavelength of the the frequency and wavelength of the source? source?

SITUATION SITUATION 22 Stationary Source; Moving Stationary Source; Moving ObserversObservers

• Observer 1 moves a distance Observer 1 moves a distance vvoott toward the source at toward the source at speed speed vvoo • We had known earlier that wavefronts also move at We had known earlier that wavefronts also move at speedspeed v v towards O towards O11 in time t at distance in time t at distance vtvt. The distance . The distance traveled by the wavefronts with respect to Otraveled by the wavefronts with respect to O11 becomes becomes vtvt + + vvOOtt. . • The number of wavelengths intercepted by OThe number of wavelengths intercepted by O11 at this at this distance is (distance is (vt + v0tvt + v0t)/ λ.)/ λ.

From equation (1), we have λ = v/ f, f’ becomes

(3)

This shows that there is an increase in the frequency f’ heard by O1 as it goes nearer to the sound source as given by,

(2)

• If observer 2 moves away from the sound source, the distance traveled by the wavefronts with respect to O2 in time t, is vt – vot. • Consequently, there would be a decrease in the frequency heard by O2 as given by,

(4)

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

(5)

(STATIONARY SOURCE; MOVING OBSERVER)

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

SITUATIONSITUATION 3 3 Moving Source; Stationary Moving Source; Stationary ObserversObservers

• As the source moves a distance vST (T=1/f period of wave) toward O1 there is a decrease in the wavelength of sound by a quantity of vsT.• The shortened wavelength λ’ becomes

λ’ = λ – vsT

The frequency The frequency f’ f’ of sound wave heard by Oof sound wave heard by O1 1 increases increases as given by,as given by,

(6)

• With respect to observer 2, the wavelength of sound increases, where λ’ becomes λ + vsT. •The frequency f’ of sound wave heard by O2 decreases as given by,

(7)

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

(8)

(MOVING SOURCE; STATIONARY OBSERVER)

SITUATION 4 Moving Source and Observer

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

(MOVING SOURCE AND OBSERVER)

(9)

(9)

The ± signs correspond to the direction of the source or observer when they are moving relative to the other. These would determine whether there is an increase or decrease on the frequency heard by the observer during the motion.

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

• If vIf voo> v> vs s , 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

(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> vs s , decrease in observed frequency, decrease in observed frequency If vIf voo< v< vss , increase in observed frequency , increase in observed frequency

That’s all folks!That’s all folks!