Question 54: Waves

Question

A person driving car at a constant speed of $$15 \mathrm{~m} / \mathrm{s}$$ is approaching a vertical wall. The person notices a change of $$40 \mathrm{~Hz}$$ in the frequency of his car's horn upon reflection from the wall. The frequency of horn is _______________ $$\mathrm{Hz}$$.
(Given: Speed of sound : $$330 \mathrm{~m} / \mathrm{s}$$ )

Accepted Answer

$$
\begin{aligned}
& 	ext { Frequency of reflected sound }=\left(\frac{v+v_{\mathrm{c}}}{v-v_c}ight) f_0 \\
& f=\left(\frac{330+15}{330-15}ight) 	imes f_0 \\
& =\frac{345}{315} f_0 \\
& \frac{345}{315} f_0-f_0=40 \\
& \frac{30}{315} f_0=40 \\
& f_0=\frac{4 	imes 315}{3}=420 \mathrm{~Hz}
\end{aligned}
$$

Waves

Integer / Numeric Answer Type