An observer is moving on a circular path of radius `r` with speed `V_(0)` around source kept at centre. The apparent frequency observed by observer is (n is actual frequency)

Options

A. greater than n
B. less than n
C. `n`
D. no sound is heard

Explanation

To solve the problem of finding the apparent frequency observed by an observer moving in a circular path around a source of sound, we can follow these steps:

### Step 1: Understand the Setup
We have a source of sound located at the center of a circular path with radius \( r \). The observer is moving along this circular path with a speed \( V_0 \). The actual frequency emitted by the source is \( n \).

### Step 2: Analyze the Motion
The observer's motion is circular, meaning at any point on the path, the velocity of the observer is directed tangentially to the circle. The line connecting the observer to the source is radial.

### Step 3: Apply the Doppler Effect
The Doppler effect describes how the frequency of a wave changes for an observer moving relative to the source of the waves. The formula for the apparent frequency \( f' \) when there is relative motion is given by:

\[ f' = f \frac{v + v_o}{v - v_s} \]

where:
- \( f' \) is the apparent frequency,
- \( f \) is the actual frequency (which is \( n \) in this case),
- \( v \) is the speed of sound,
- \( v_o \) is the speed of the observer,
- \( v_s \) is the speed of the source.

### Step 4: Determine the Relative Velocities
In this scenario:
- The source is stationary, so \( v_s = 0 \).
- The observer is moving at speed \( V_0 \) tangentially to the circular path, which means the direction of \( V_0 \) is perpendicular to the line joining the observer and the source.

### Step 5: Conclusion on Apparent Frequency
Since the observer's velocity is perpendicular to the line connecting them to the source, it does not affect the frequency of the sound waves reaching the observer. Therefore, the apparent frequency remains equal to the actual frequency:

\[ f' = n \]

### Final Answer
The apparent frequency observed by the observer is \( n \).

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