Question

A speaker emits a sound wave of frequency $f_0$. When it moves towards a stationary observer with speed $u$. The observer measures a frequency $f_1$. If the speaker is stationary, and the observer moves towards it with speed $u$, the measured frequency is $f_2$. Then.

• A. $f_1=f_2<f_0$
• B. $f_1>f_2$
• C. $f_1<f_2$
• D. $f_1=f_2>f_0$

Answer 1

The correct option is B $f_1>f_2$

Let the speed of sound in air be $v$.

Using Doppler effect when the source moves towards the stationary observer.

Apparent frequency heard $f_1=f_o[\frac{v_{sound}}{v_{sound}-v_{source}}]$

$\therefore$ $f_1=f_o[\frac{v}{v-u}]=f_o[1+\frac{u}{v-u}]$

Using Doppler effect when the observer moves towards the stationary source.

Apparent frequency heard by observer $f_2=f_o[\frac{v_{sound}+v_{observer}}{v_{sound}}]$

$\therefore$ $f_2=f_o[\frac{v+u}{v}]=f_o[1+\frac{u}{v}]$

$⟹$ $f_1>f_2$