Question

A friend of yours is loudly singing a single note at 412 Hz while racing toward you at 23.0 m/s on a day when the speed of sound is 344 m/s.a. What frequency do you hear?b. What frequency does your friend hear if you suddenly start singing at 420 Hz?

Answer 1

Doppler Effect is required to solve the problem. The Doppler effect is the change in the perceived frequency of any wave movement when the emitter, or focus of waves, and the receiver, or observer, move relative to each other. The general formula of observed frequency, due to Doppler's effect is as follows,

$f_0 = (\frac{v+v_0}{v-v_s})f_s$

$f_0$ = Frequency observed by observer

v = Velocity of Sound

$v_0$ = Velocity of observer

$v_s$ = Velocity of source

$f_s$ = Frequency of source

PART A) Replacing our values we have that,

$f_0 = (\frac{v+v_0}{v-v_s})f_s$

$f_0 = (\frac{344+0}{344-23})(412)$

$f_0 = 441.52Hz$

PART B) Here the same procedure is performed but this time repeated in the opposite direction.

$f_0 = (\frac{v+v_0}{v-v_s})f_s$

$f_0 = (\frac{344+23}{344-0})(420)$

$f_0 = 448.08Hz$