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If the source is moving, the wavelength of sound in air changes but does it change the duration for which the stationary observer hears the sound? Like say if the source moving at velocity $V$ emits sound for $T$ seconds, does the stationary observer also hear the sound for $T$ seconds only?

I tried solving by assuming the distance between moving source $s$ and stationary observer $o$ as $d$. The fist sound wave reaches the observer at $time = d/v$ where $v$ is the velocity of sound in air. The last sound wave emitted at $time = T seconds$ reaches the observer in $time = (d-VT)/v$ seconds. So the time duration for which the ‘o’ hears the sound comes out to be $T(v-V)/v$ seconds. But I think it’s incorrect. So, could someone please help me out with this ?

And also what happens to the time duration of hearing the sound if the observer is moving?

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Does velocity of source affect the duration for which the observer hears the sound?

Yes. If the source is moving away, the pitch of the sound will decrease, but also the duration of the sound will be longer.

If the source is moving nearer, the pitch of the sound will increase, and the duration of the sound will be shorter.

And also what happens to the time duration of hearing the sound if the observer is moving?

The same principle applies. If the pitch goes up, the duration will be shorter. If the pitch goes down, the duration will be longer.

You can think of it this way. The same number of wave-crests will impinge on the listener regardless of relative motion. So, if there is a longer time between wave-crests, the sound will last longer, and vice-versa.

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  • $\begingroup$ Is there any mathematical relation between the time duration of sound being heard by observer and time duration for which the source emits the sound if the source or observer are moving with some velocity ? And thanks! $\endgroup$
    – Nil
    Apr 27, 2021 at 2:02
  • $\begingroup$ So, can we say that the ratio of time period for which the observer hears the sound to the time period for which the source emits the sound is equal to inverse of the ratio of the frequency heard to the original frequency? $\endgroup$
    – Nil
    Apr 27, 2021 at 13:44
  • $\begingroup$ @Nil "So, can we say that the ratio of time period for which the observer hears the sound to the time period for which the source emits the sound is equal to inverse of the ratio of the frequency heard to the original frequency?" Yes. $\endgroup$ Apr 27, 2021 at 13:45

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