Question

A police car with a siren of frequency $8kHz$ is moving with uniform velocity $36km/hr$ towards a tall building which reflects the sound waves. The speed of sound in air is $320m/s$. The frequency of the siren heard by the car driver is:

• A. $8.50kHz$
• B. $8.25kHz$
• C. $7.75kHz$
• D. $7.50kHz$

Answer 1

The correct option is A $8.50kHz$

Frequency received by the building

$f^{\prime }=f\left[\frac{c}{c-v}\right]$

$\Rightarrow f^{\prime }=8\left[\frac{320}{310}\right]$

Now wall becomes source and driver hears the frequency

$f^{\prime \prime }=f\left[\frac{c+v}{c}\right]$

$\Rightarrow f^{\prime \prime }=\frac{8\times 320}{310}\approx 8.5kHz$