Question

a) A siren blares an apparent frequency of 1200 Hz as it drives toward you a 30 m/s. If you are standing still, what is the actual frequency of the siren? What frequency do you hear as it is driving away from you?

b)When two trumpets play the same note, a tuner measures a beat frequency of 2 Hz. If one trumpet is playing a 440 Hz note, what frequency is the other trumpet playing?

Answer 1

A) so apparant freaquany is given by Doppler shift when source is moving towards us by the formula,

Here f' = 1200 Hz.

v is speed of sound = 340 m/s

And speed of source Vs = 30 m/s

So we get actual frequency f as

Similarly if source is now moving away then formula changes as

So we get,

So we get,

f = 1305.88 Hz

2) so if beat freaquany is ∆f = 2Hz

So,. If frequency of one trumpet

f= 440 Hz

So, freaquany of second trumpet is

Either f+∆f or f-∆f

So 438 Hz or 442 Hz