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 of determining the frequency of sound heard by the listener when a bus is moving in a circle around them, we can follow these steps:

### Step 1: Understand the scenario
The bus is moving in a circular path around a listener with a speed of 20 m/s and a radius of 2 m. The bus driver blows a horn with a frequency of 210 Hz. The listener is positioned at the center of the circular path.

### Step 2: Identify the parameters
- Speed of the bus (v) = 20 m/s
- Radius of the circular path (r) = 2 m
- Frequency of the horn (f₀) = 210 Hz

### Step 3: Determine the relative motion
Since the bus is moving in a circular path, the listener is at the center, and the distance between the listener and the bus remains constant at 2 m. This means that there is no change in distance as the bus moves around the listener.

### Step 4: Apply the Doppler Effect
In the case of the Doppler Effect, the frequency heard by the observer (listener) can be affected by the relative motion of the source (bus) and the observer (listener). However, since the distance between the bus and the listener remains constant, there is no relative velocity component affecting the frequency.

### Step 5: Conclude the frequency heard by the listener
Since there is no change in distance and no relative motion affecting the sound waves, the frequency of sound heard by the listener will be equal to the frequency of the sound emitted by the bus. Therefore, the frequency heard by the listener (f') is equal to the frequency of the horn (f₀).

\[ f' = f₀ = 210 \text{ Hz} \]

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

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