A car blowing a horn of frequency 350 Hz is moving normally towards a wall a speed of 5 m/s The beat frequency heard by a person standing between the car and wall is (speed of sound in air =350 m/s )

Options

A. 1
B. 0
C. 3
D. 4

Answer

To solve the problem, we need to find the beat frequency heard by a person standing between a car blowing a horn and a wall. The car is moving towards the wall at a speed of 5 m/s, and the frequency of the horn is 350 Hz. The speed of sound in air is given as 350 m/s.

### Step-by-Step Solution:

1. **Identify the Frequencies:**
- The frequency of the horn (source frequency, \( f_0 \)) is given as 350 Hz.
- The speed of sound in air (\( v \)) is 350 m/s.
- The speed of the car (source speed, \( v_s \)) is 5 m/s.
- The observer (the person) is stationary.

2. **Calculate the Frequency Heard by the Person Directly from the Car (\( f_1 \)):**
- Since the car is moving towards the observer, we can use the Doppler effect formula:
\[ f_1 = f_0 \left( \frac{v + v_o}{v - v_s} \right) \]
- Here, \( v_o = 0 \) (the observer is stationary), so the formula simplifies to:
\[ f_1 = f_0 \left( \frac{v}{v - v_s} \right) \]
- Plugging in the values:
\[ f_1 = 350 \left( \frac{350}{350 - 5} \right) = 350 \left( \frac{350}{345} \right) \]
- Calculating \( f_1 \):
\[ f_1 \approx 350 \times 1.0145 \approx 354.08 \text{ Hz} \]

3. **Calculate the Frequency Heard by the Person from the Reflected Sound (\( f_2 \)):**
- The sound wave travels to the wall and reflects back. The wall acts as a stationary observer for the sound wave coming from the car.
- The frequency of the sound reaching the wall (\( f_3 \)) can be calculated using the same Doppler effect formula:
\[ f_3 = f_0 \left( \frac{v + 0}{v - v_s} \right) = f_0 \left( \frac{v}{v - v_s} \right) = 350 \left( \frac{350}{345} \right) \]
- Thus, \( f_3 \) is also approximately 354.08 Hz.

4. **Calculate the Frequency Heard by the Person from the Reflected Sound (\( f_2 \)):**
- The frequency \( f_2 \) is the frequency of the sound reflected back to the observer:
\[ f_2 = f_3 \left( \frac{v + v_o}{v - 0} \right) = f_3 \left( \frac{v}{v} \right) = f_3 \]
- Therefore, \( f_2 \approx 354.08 \text{ Hz} \).

5. **Calculate the Beat Frequency:**
- The beat frequency is given by the difference between the two frequencies:
\[ f_{beat} = |f_2 - f_1| \]
- Since \( f_1 \) and \( f_2 \) are approximately equal:
\[ f_{beat} = |354.08 - 354.08| = 0 \text{ Hz} \]

### Final Answer:
The beat frequency heard by the person standing between the car and the wall is **0 Hz**.