Question

A police car moving at 30 m/s, chases a motorcyclist. The police man sounds his horn at 180 Hz while both of them move towards a stationary siren of frequency 160 Hz. Calculate the speed of the motorcyclist, if it is given that he does not observe any beats (take, the speed of sound = 330 m/s).

• A. 25 m/s
• B. 30 m/s
• C. 40 m/s
• D. 35 m/s

Answer 1

The correct option is D 35 m/s

Case (i),
$f_1=f_0\left(\frac{Vs-U_0}{Vs-U_s}\right)$
$=f_0\left(\frac{330-U}{330-30}\right)=180\frac{(330-U)}{300}$
$f_1=180\left(\frac{330-U}{330}\right)...\left(i\right)$
Case (ii), $f_2=160\left(\frac{330+U}{330}\right)...\left(ii\right)$
$\because$ There is no beats
$\therefore f_1=f_2$
$180\left(\frac{330-U}{300}\right)=160\left(\frac{330+U}{330}\right)$
$\Rightarrow 9\left(\frac{330-U}{300}\right)=160\left(\frac{330+U}{330}\right)$
$\Rightarrow \frac{9}{10}(330-U)=\frac{8}{11}(330+U)$
$\Rightarrow 32670-99U=26400+80U$
$\therefore U=\frac{6270}{179}=35.02m/s$