A car is moving with `90 km h^(-1)` blows a horn of 150 Hz, towards a cliff. The frequency of the reflected sound heard by the driver will be (speed of sound in air is `340 ms^(-1)` )

Options

A. 150 Hz
B. 140 Hz
C. 180 Hz
D. 174 Hz

Answer

To solve the problem, we need to find the frequency of the reflected sound heard by the driver of the car moving towards a cliff. We'll use the Doppler effect formula for sound.

### Step-by-Step Solution:

1. **Convert the speed of the car from km/h to m/s:**
\[ \text{Speed of the car} = 90 \text{ km/h} = 90 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 25 \text{ m/s} \]

**Hint:** Remember that to convert km/h to m/s, multiply by \( \frac{5}{18} \).

2. **Identify the parameters:**
- Speed of sound in air, \( v = 340 \text{ m/s} \)
- Frequency of the horn, \( f = 150 \text{ Hz} \)
- Speed of the observer (the driver), \( v_o = 25 \text{ m/s} \) (since the car is moving towards the cliff)
- Speed of the source (the cliff), \( v_s = 0 \text{ m/s} \) (the cliff is stationary)

3. **Calculate the apparent frequency when the sound reaches the cliff:**
Using the Doppler effect formula:
\[ f' = f \frac{v + v_o}{v - v_s} \]
Substituting the values:
\[ f' = 150 \frac{340 + 25}{340 - 0} = 150 \frac{365}{340} \]

**Hint:** When calculating the apparent frequency, ensure you correctly identify which object is the source and which is the observer.

4. **Calculate \( f' \):**
\[ f' = 150 \times \frac{365}{340} = 150 \times 1.0735 \approx 160.98 \text{ Hz} \]

5. **Now, this frequency \( f' \) acts as the source frequency when the sound reflects back to the car. Calculate the frequency heard by the driver:**
Using the Doppler effect formula again, but now the car is the observer and the cliff is the source:
\[ f'' = f' \frac{v + v_o}{v - v_s} \]
Substituting the values:
\[ f'' = 160.98 \frac{340 + 25}{340 - 0} = 160.98 \frac{365}{340} \]

**Hint:** Remember that the roles of source and observer switch when the sound reflects.

6. **Calculate \( f'' \):**
\[ f'' = 160.98 \times \frac{365}{340} \approx 160.98 \times 1.0735 \approx 172.87 \text{ Hz} \]

7. **Final Result:**
Rounding to the nearest whole number, the frequency of the reflected sound heard by the driver is approximately:
\[ f'' \approx 173 \text{ Hz} \]

### Conclusion:
The frequency of the reflected sound heard by the driver will be approximately **173 Hz**.