An observer is standing $500 \mathrm{~m}$ away from a vertical hill. Starting between the observer and the…
An observer is standing $500 \mathrm{~m}$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000 \mathrm{~Hz}$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 \mathrm{~Hz}$, the frequency of the sound heard after reflection from the hill (in Hz) is about, (velocity of sound $=330 \mathrm{~ms}^{-1}$ ) :
1042
1032
1022
1012
Solution
Sound heard directly
$f_1=f_o\left(\frac{v}{v+v_s}\right)$
$\therefore \quad 970=1000\left(\frac{330}{330+v_s}\right)$
or $\quad v_s=10.2 \mathrm{~m} / \mathrm{s}$
The frequency of reflected sound is given by
$f_2=f_o\left(\frac{v}{v-v_s}\right)$
$=1000\left(\frac{330}{330-10.2}\right)$
$=\frac{1000 \times 330}{319.8}$
$\approx 1032 \mathrm{~Hz}$