Question

A friend of yours is loudly singing a single note at 403 Hz while racing toward you at 26.3 m/s on a day when the speed of sound is 340 m/s .What frequency do you hear?What frequency does your friend hear if you suddenly start singing at 403?

Answer 1

Answer:

Explanation:

Given

Natural frequency of vibration $f=403\ Hz$

Velocity of source $v_s=26.3\ m/s$

Considering velocity of sound $v=341\ m/s$

Apparent Frequency of sound is given by Doppler effect

$f'=\frac{v+v_o}{v-v_s}\cdot f$

where $f=natural\ frequency$

$v=velocity\ of\ sound\ wave$

$v_o=velocity\ of\ observer$

$v_s=velocity\ of\ source$

$f'=apparent\ frequency$

here $v_o=0$

$f'=\frac{341}{341-26.3}\cdot 403=437.37 Hz$

If you start singing at frequency of 403 Hz then apparent frequency to your friend

Observer is moving with 26.3 m/s and source is stationary

$f'=\frac{v+26.3}{v-0}\cdot 403$

$f'=\frac{341+26.3}{341}\cdot 403=434.08\ Hz$