The minimum intensity of sound is zero at a point due to two sources of nearly equal frequencie4s when

Options

A. (a)two sources are vibration in the opposite phase
B. (b)the amplitude of two sources are equal
C. (c)at the point of observation, the amplitudes of two S.H.M. produced by two sources are equal and both the S.H.M. are along the same straight line
D. (d)both the sources are in the same phase

Answer

To solve the question regarding the minimum intensity of sound being zero at a point due to two sources of nearly equal frequencies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Intensity**:
The intensity of sound (I) is related to the amplitude (A) of the sound wave. The formula for intensity is given by:
\[ I \propto A^2 \]
This means that the intensity is proportional to the square of the amplitude.

2. **Condition for Minimum Intensity**:
For the minimum intensity of sound to be zero, the combined effect of the two sound waves must cancel each other out completely. This occurs when the two waves are in opposite phases.

3. **Equal Amplitudes**:
If two sound waves have equal amplitudes and they are 180 degrees out of phase (i.e., they are perfectly destructive), the resultant amplitude will be zero. Thus, the intensity will also be zero:
\[ I_{\text{min}} = 0 \quad \text{when} \quad A_1 = A_2 \quad \text{and} \quad \text{phase difference} = 180^\circ \]

4. **Direction of Propagation**:
The two sources must be emitting sound waves in the same straight line for the cancellation to occur effectively. If they are not aligned, the waves may not meet in such a way that they completely cancel each other out.

5. **Conclusion**:
Therefore, the minimum intensity of sound is zero at a point due to two sources of nearly equal frequencies when the amplitudes of the waves are equal and they are aligned in the same direction.

### Final Answer:
The correct option is **C**: The amplitudes of the sound waves are equal and they propagate in the same straight line.

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