Question

The driver of a car traveling at a speed of $30\frac{m}{s}$ towards a hill sounds a horn of frequency $600Hz$. If the velocity of sound in air is $330\frac{m}{s}$, the frequency of reflected sound as heard by the driver is then

Answer 1

Step 1: The car acts as the source and the hill act as the source

By, the doppler effect apparent frequency is

$f^{\text{'}}=\frac{v}{v-v_c}\times f$

$f^{\text{'}}=$Apparent frequency

$f=$ Frequency of horn

$v=$the velocity of sound in air

$v_c=$ the velocity of the car

$$\begin{gathered} \Rightarrow f\text{'}=\frac{330}{330-30}\times 600 \\ \Rightarrow f\text{'}=660Hz \end{gathered}$$

Step 2: In the reflection hill act as a source and the car as the listener

$f"=\frac{\left(v+v_c\right)}{v}\times f\text{'}$

$f"=$ Reflected frequency heard by the driver

$$\begin{gathered} \Rightarrow f"=\frac{\left(330+30\right)}{330}\times 660 \\ \Rightarrow f"=720Hz \end{gathered}$$

Hence, the frequency of reflected sound heard by driver is $720Hz$.