Question

A car moving with a velocity of $36km{h}^{-1}$ crosses a siren of frequency $500Hz$. The apparent frequency of siren after passing it will be

• A. $520Hz$
• B. $485Hz$
• C. $540Hz$
• D. $460Hz$

Answer 1

The correct option is B

$485Hz$

Step 1. Given data

Velocity of the car, $v=36km{h}^{-1}$

$v=10m{s}^{-1}$

Frequency, $f=500Hz$

Step 2. Finding the apparent frequency

By using the formula of apparent frequency, $f^{\text{'}}$

$f^{\text{'}}=f\left(\frac{v_s-v}{v_s}\right)$

Where, $v_s=330m{s}^{-1}$ is the velocity of sound

$f^{\text{'}}=500\times \left(\frac{330-10}{330}\right)$

$f^{\text{'}}=484.5Hz$

By rounding off,

$f^{\text{'}}=485Hz$

Therefore, the apparent frequency is $485Hz$

Hence, the correct option is $\left(B\right)$