Question

A police bike with its siren on, moving with a velocity $v_s$ toward a man standing at a bus stop. As the bike approaches, the man hears the sound at a frequency of $f_d$. Take the speed of sound to be $v$.
Calculate the frequency produced by the siren?

• A. $\frac{v-v_s}{v}{f}_d$
• B. $\frac{v}{v-v_s}{f}_d$
• C. $\frac{v+v_s}{v}{f}_d$
• D. $\frac{v-v_s}{v+v_s}{f}_d$
• E. $\frac{v}{v+v_s}{f}_d$

Answer 1

Answer: (A)

$\frac{v-v_s}{v}{f}_d$

Speed of sound $=v$

Speed of sound source $=v_s$

Apparent frequency heard by the man (observer) $=f_d$

Using Doppler effect in case when the source moves towards the stationary observer :

$\therefore$ $f_d=f[\frac{v}{v-v_s}]$ $⟹f=\frac{v-v_s}{v}{f}_d$