Question

you are standing by the side of the road as a fire engine approaches you. because of the doppler shift, you hear the engines siren at a higher frequency than it was emitted at. how would your sensation of the pitch of the sirens sound change if you ran toward the moving engine? how would your sensation of the pitch of the sirens sound change if you instead ran with the same velocity as the engine?

Answer 1

When there is a relative motion between the source and observer, the frequency of sound heard by the observer is different from the frequency actually emitted by the source which is known as Doppler's effect. The Doppler efffect says that if f' be the apparent frequency of sound heard by observer and f is the original frequency emitted by the source, then,

   f' = [(v+vo)/(v-vs)] * f

when both observer and source are approaching each other, where v, vo, vs are the speed of sound, observer and source respectively.

Clearly, f'>f, or in other words, when you run towards the engine the pitch of the siren heard by you will be greater than the actual pitch of the siren emitted by the source.

When you run with the same speed as the engine there will be no relative motion between you and the engine or your relative velocity with respect to the engine = 0. Hence there will be no doppler effect. So you will heard the original pitch of the siren as it is emitted by the engine.