a bus is moving with a velocity 4 m/s towards a wall, the driver sounds a horn of frequency 173 Hz . if the speed of sound in air is 350 m/s. the number of beat heard per second by a passanger on the bus will be

Options

A. one
B. two
C. three
D. four

Answer

To solve the problem, we will use the Doppler effect to find the frequencies of the sound heard by the passenger on the bus and then calculate the beat frequency.

### Step-by-Step Solution:

1. **Identify Given Data**:
- Frequency of the horn, \( f_0 = 173 \, \text{Hz} \)
- Speed of sound in air, \( v = 350 \, \text{m/s} \)
- Speed of the bus (source), \( v_s = 4 \, \text{m/s} \)

2. **Calculate the Frequency of Sound Reflected from the Wall**:
- When the bus moves towards the wall, the frequency of the sound heard by the wall (acting as a stationary observer) can be calculated using the Doppler effect formula:
\[ f_1 = f_0 \cdot \frac{v}{v - v_s} \]
- Substitute the values:
\[ f_1 = 173 \, \text{Hz} \cdot \frac{350 \, \text{m/s}}{350 \, \text{m/s} - 4 \, \text{m/s}} = 173 \, \text{Hz} \cdot \frac{350}{346} \]
- Calculate \( f_1 \):
\[ f_1 \approx 173 \, \text{Hz} \cdot 1.0115 \approx 175 \, \text{Hz} \]

3. **Calculate the Frequency Heard by the Passenger**:
- Now, the wall reflects the sound back to the bus. The bus (passenger) is moving towards the wall, so we again use the Doppler effect:
\[ f_2 = f_1 \cdot \frac{v + v_s}{v} \]
- Substitute the values:
\[ f_2 = 175 \, \text{Hz} \cdot \frac{350 \, \text{m/s} + 4 \, \text{m/s}}{350 \, \text{m/s}} = 175 \, \text{Hz} \cdot \frac{354}{350} \]
- Calculate \( f_2 \):
\[ f_2 \approx 175 \, \text{Hz} \cdot 1.0114 \approx 177 \, \text{Hz} \]

4. **Calculate the Beat Frequency**:
- The beat frequency is the difference between the frequency heard by the passenger and the original frequency of the horn:
\[ f_{\text{beat}} = f_2 - f_0 = 177 \, \text{Hz} - 173 \, \text{Hz} = 4 \, \text{Hz} \]

### Final Answer:
The number of beats heard per second by a passenger on the bus is \( \boxed{4} \, \text{Hz} \).