Question

Two cars A and B approach a stationary observer from opposite sides as shown in figure. Observer hears no beats. If the frequency of the horn of the car Bis 504 Hz, the frequency of horn of car A will be

• A. 529.2 Hz
• B. 295.2 Hz
• C. 440.5 Hz
• D. 259.2 Hz

Answer 1

Answer: (A)

From Doppler's effect, the apparent change in frequency of a wave that is perceived by stationary observer is
$20mm{n}^{\prime }=n_0\left(\frac{v}{v-v_s}\right)$
where, v is speed of sound
Since, observer is not hearing any beats, the apparent
frequency of the two cars should be equal
$\therefore 30mm{n}^{\prime }=n^{\prime \prime }$
$20mm504\left(\frac{v}{v-v_s}\right)=n\left(\frac{v}{v-15}\right)$
$\therefore n=\frac{(330-15)\times 504}{(330-30)}$
$40mm=\frac{315\times 504}{330}=529.2Hz$