A source of sound moves towards a listener with a velocity equal to that of sound. If the source emits n waves per second, then the listener moving away from the source with the same velocity receives

Options

A. n waves per sec
B. 2n waves per sec
C. zero waves per sec
D. `n//2`

Explanation

To solve the problem, we need to analyze the situation using the principles of wave motion and the Doppler effect. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the scenario
We have a source of sound that is moving towards a listener at the speed of sound (let's denote this speed as \( v \)). The source emits \( n \) waves per second. The listener is also moving away from the source at the same speed \( v \).

### Step 2: Identify the parameters
- Speed of sound = \( v \)
- Speed of the source (moving towards the listener) = \( v_s = v \)
- Speed of the listener (moving away from the source) = \( v_o = v \)
- Frequency of the source = \( n \)

### Step 3: Apply the Doppler effect formula
The apparent frequency \( f' \) observed by the listener can be calculated using the Doppler effect formula:
\[ f' = f \cdot \frac{v + v_o}{v - v_s} \]
Where:
- \( f \) is the actual frequency emitted by the source (which is \( n \)).
- \( v \) is the speed of sound.
- \( v_o \) is the speed of the observer (listener).
- \( v_s \) is the speed of the source.

### Step 4: Substitute the values
Since both the listener and the source are moving at the speed of sound, we substitute \( v_o = v \) and \( v_s = v \) into the formula:
\[ f' = n \cdot \frac{v + v}{v - v} = n \cdot \frac{2v}{0} \]

### Step 5: Analyze the result
The denominator becomes zero, which indicates that the apparent frequency \( f' \) approaches infinity. However, in practical terms, this means that the listener is moving away at the same speed as the sound waves are reaching him, resulting in no waves being received.

### Conclusion
Thus, the listener receives **0 waves per second**.

### Final Answer
The correct option is **0 waves per second**.

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