Question

An observer is standing $500m$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is 970Hz, the frequency of the sound heard after reflection from the hill (in Hz) is about, (velocity of sound = $330m{s}^{-1}$)

• A. $1042$
• B. $1032$
• C. $1022$
• D. $1012$

Answer 1

The correct option is B $1032$

Hill acts as a source with sound frequency.

$f^1=\left(\frac{v}{v-v_s}\right)f$

Frequency of sound directly heard, $f^2=\left(\frac{v}{v+v_s}\right)f$

$\Rightarrow 970=\left(\frac{330}{330+v_s}\right)1000$

$\Rightarrow 330+v_s=340$

$\Rightarrow v_s=10m{s}^{-1}$

$\therefore f^1=\left(\frac{330}{320}\right)\times 1000=1032Hz.$