Question

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

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

Answer 1

Answer: (B)

Sound heard directly
$f_{1} =f_{o}\left(\frac{v}{v+v_{s}}\right)$
$\therefore 970 =1000\left(\frac{330}{330+v_{s}}\right)$
or $v_{s}=10.2 \,m / s$
The frequency of reflected sound is given by
$f_{2}=f_{o}\left(\frac{v}{v-v_{s}}\right) $
$=1000\left(\frac{330}{330-10.2}\right) $
$=\frac{1000 \times 330}{319.8} $
$\approx 1032 \,Hz$