The driver of a car travelling with speed `30ms^-1` towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is `330ms^-1`, the frequency of reflected sound as heard by driver is

Options

A. 550 Hz
B. 555.5 Hz
C. 720 Hz
D. 500 Hz

Answer

To solve the problem, we will use the Doppler effect formula for sound waves. The scenario involves a car moving towards a hill (which acts as a reflecting surface) and the driver hearing the reflected sound.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Speed of the car (source) \( V_s = 30 \, \text{m/s} \)
- Frequency of the horn \( f = 600 \, \text{Hz} \)
- Speed of sound in air \( V = 330 \, \text{m/s} \)

2. **Calculate the Apparent Frequency of Sound Striking the Hill:**
Since the car is moving towards the hill, we will use the Doppler effect formula for a moving source and a stationary observer (the hill):
\[ f' = \frac{V}{V - V_s} \cdot f \]
Substituting the values:
\[ f' = \frac{330}{330 - 30} \cdot 600 \]
\[ f' = \frac{330}{300} \cdot 600 \]
\[ f' = 1.1 \cdot 600 = 660 \, \text{Hz} \]

3. **Calculate the Frequency of the Reflected Sound as Heard by the Driver:**
Now, the hill acts as a source of sound reflecting back to the driver, who is moving towards the hill. We will apply the Doppler effect formula again, but this time the driver is the observer moving towards the source (the hill):
\[ f'' = \frac{V + V_s}{V} \cdot f' \]
Substituting the values:
\[ f'' = \frac{330 + 30}{330} \cdot 660 \]
\[ f'' = \frac{360}{330} \cdot 660 \]
\[ f'' = 1.0909 \cdot 660 \approx 720 \, \text{Hz} \]

4. **Final Result:**
The frequency of the reflected sound as heard by the driver is approximately \( 720 \, \text{Hz} \).