A source is moving with a constant speed of 10 m/s on a circular track of 200 m. It emits a sound of frequency 200 Hz. A listener stands at the centre of the circular track. The frequency received by the listener is (velocity of sound = 340 m/s)

Options

A. zero
B. 200 Hz
C. 190 Hz
D. 210 Hz

Answer

To solve the problem, we need to determine the frequency of sound received by a listener standing at the center of a circular track where a source is moving with a constant speed. Here’s a step-by-step solution:

### Step 1: Understand the scenario
The source of sound is moving in a circular path with a radius derived from the circumference of the circular track. The listener is at the center of this circular track.

**Hint:** Visualize the circular track and the positions of the source and listener to understand the geometry involved.

### Step 2: Identify the parameters
- Speed of the source (v_source) = 10 m/s
- Frequency of the sound emitted (f_source) = 200 Hz
- Velocity of sound in air (v_sound) = 340 m/s

**Hint:** Write down all the given values clearly to avoid confusion later.

### Step 3: Analyze the motion of the source
As the source moves in a circular path, its velocity is always directed tangentially to the circle. The listener, being at the center, will not experience any change in frequency due to the motion of the source.

**Hint:** Remember that the Doppler effect depends on the relative motion between the source and the observer. Here, the motion is perpendicular.

### Step 4: Determine the frequency received by the listener
Since the source is moving tangentially and the listener is at the center, the component of the source's velocity along the line connecting the source to the listener is zero. Therefore, the frequency of sound received by the listener remains unchanged.

**Hint:** Consider how the Doppler effect applies when the source is moving directly towards or away from the observer versus when it is moving perpendicular to the line of sight.

### Step 5: Conclusion
The frequency received by the listener is the same as the frequency emitted by the source:
- Frequency received (f_received) = f_source = 200 Hz

**Hint:** Always check if the conditions of the problem allow for any changes in frequency due to motion.

### Final Answer
The frequency received by the listener is **200 Hz**.

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