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`

Explanation

To find the frequency of the reflected sound as heard by the driver of the car, we will use the Doppler effect formula. The situation involves the driver moving towards a stationary object (the hill), which reflects the sound back to the driver.

### Step-by-Step Solution:

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

2. **Calculate the Frequency of the Sound as Heard by the Hill:**
The frequency heard by the hill (which acts as a stationary observer) can be calculated using the Doppler effect formula for a moving source:
\[ f' = f_s \left( \frac{v}{v - v_o} \right) \]
Here, \( f' \) is the frequency heard by the hill, and since the hill is stationary, we substitute the values:
\[ f' = 600 \left( \frac{330}{330 - 30} \right) \]
\[ f' = 600 \left( \frac{330}{300} \right) \]
\[ f' = 600 \times 1.1 = 660 \, \text{Hz} \]

3. **Calculate the Frequency of the Reflected Sound as Heard by the Driver:**
Now, the hill reflects this frequency back to the driver. The driver is now the observer moving towards the source of the reflected sound (the hill). We again use the Doppler effect formula:
\[ f'' = f' \left( \frac{v + v_o}{v} \right) \]
Substituting the values we have:
\[ f'' = 660 \left( \frac{330 + 30}{330} \right) \]
\[ f'' = 660 \left( \frac{360}{330} \right) \]
\[ f'' = 660 \times 1.0909 \approx 720 \, \text{Hz} \]

### Final Answer:
The frequency of the reflected sound as heard by the driver is approximately **720 Hz**.