Question

An ambulance driving with velocity $\frac{v_1}{8}$ where $v_1$ is the speed of sound, emits a siren with a frequency of f. What is the frequency heard by a stationary observer toward whom the ambulance is driving?

• A. $\frac{f}{8}$
• B. $\frac{7f}{8}$
• C. $f$
• D. $\frac{8f}{7}$
• E. $8f$

Answer 1

The correct option is D $\frac{8f}{7}$

We know from Doppler's effect in sound that when a source of sound approaches to a stationary observer , the apparent frequency of sound heard by observer is given by ,

$f^{\prime }=f\frac{v}{v-v_s}$ ,

where $f=$ original frequency of sound ,

$v=$ velocity of sound ,

$v_s=$ velocity of source of sound ,

now if $v_s=v/8$ ,

then apparent frequency heard by observer $f^{\prime }=f\frac{v}{v-v/8}$ ,

or $f^{\prime }=f\frac{v}{7v/8}$ ,

or $f^{\prime }=8f/7$