a bus is moving in a circle around a listener with speed 20 m/s of radius 2 m. Bus driver blows a horn with frequency 210 Hz. the frequency of sound heard by the listener is

Options

A. 212 Hz
B. 210 Hz
C. 218 Hz
D. 420 Hz

Answer

To solve the problem, we need to determine the frequency of sound heard by the listener when a bus is moving in a circle around them. We will apply the principles of the Doppler effect, but in this case, we will see that there is no change in frequency due to the nature of the motion.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Speed of the bus (v) = 20 m/s
- Radius of the circular path (r) = 2 m
- Frequency of the horn (f₀) = 210 Hz

2. **Understand the Motion:**
- The bus is moving in a circular path around the listener, who is stationary at the center of the circle.
- The distance between the listener and the bus remains constant at the radius of the circle (2 m).

3. **Determine the Effect of Motion:**
- The Doppler effect occurs when there is relative motion between the source of sound and the observer. In this case, the listener is at the center of the circle, and the bus moves around them.
- Since the distance between the bus (source) and the listener (observer) does not change, the frequency of the sound heard by the listener will not change.

4. **Conclusion:**
- The frequency of the sound heard by the listener is equal to the frequency of the sound emitted by the bus driver.
- Therefore, the frequency of sound heard by the listener is 210 Hz.

### Final Answer:
The frequency of sound heard by the listener is **210 Hz**.

---