Two sound waves have phase difference of `60^(@)`, then they will have the path difference of:

Options

A. `3 lambda`
B. `(lambda)/(3)`
C. `(lambda)/(6)`
D. `lambda`

Explanation

To find the path difference corresponding to a phase difference of \(60^\circ\) between two sound waves, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Phase Difference and Path Difference**:
The relationship between phase difference (\(\Delta \phi\)) and path difference (\(\Delta x\)) is given by the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
where \(\lambda\) is the wavelength of the sound wave.

2. **Convert the Phase Difference to Radians**:
Since the phase difference is given in degrees, we need to convert \(60^\circ\) to radians:
\[ \Delta \phi = 60^\circ = \frac{\pi}{3} \text{ radians} \]

3. **Substitute the Phase Difference into the Formula**:
Now, we can substitute \(\Delta \phi\) into the formula:
\[ \frac{\pi}{3} = \frac{2\pi}{\lambda} \Delta x \]

4. **Rearrange the Equation to Solve for Path Difference**:
To find \(\Delta x\), rearrange the equation:
\[ \Delta x = \frac{\lambda}{2} \cdot \frac{\pi/3}{2\pi} = \frac{\lambda}{2} \cdot \frac{1}{6} = \frac{\lambda}{6} \]

5. **Conclusion**:
Therefore, the path difference corresponding to a phase difference of \(60^\circ\) is:
\[ \Delta x = \frac{\lambda}{6} \]

### Final Answer:
The path difference is \(\frac{\lambda}{6}\).

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