A wave has a frequency of `120Hz`. Two points at a distance `9m` apart have a phase difference of `1080^(@)`. The velocity of the wave is

Options

A. `340m//s`
B. `300m//s`
C. `330m//s`
D. `360m//s`

Explanation

To solve the problem, we need to find the velocity of the wave using the given frequency and phase difference between two points.

### Step-by-Step Solution:

1. **Convert Phase Difference from Degrees to Radians**:
The phase difference is given as \(1080^\circ\). To convert this to radians, use the conversion factor \(\frac{\pi \text{ radians}}{180^\circ}\):
\[ \Delta \phi = 1080^\circ \times \frac{\pi \text{ radians}}{180^\circ} = 1080 \times \frac{\pi}{180} = 6\pi \text{ radians} \]

2. **Use the Relationship Between Phase Difference and Path Difference**:
The relationship between phase difference (\(\Delta \phi\)), path difference (\(d\)), and wavelength (\(\lambda\)) is given by:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot d \]
Rearranging this gives:
\[ d = \frac{\Delta \phi \cdot \lambda}{2\pi} \]

3. **Substituting Known Values**:
We know the distance \(d = 9 \text{ m}\) and \(\Delta \phi = 6\pi \text{ radians}\). Substituting these values into the equation:
\[ 9 = \frac{6\pi \cdot \lambda}{2\pi} \]
Simplifying this:
\[ 9 = 3\lambda \implies \lambda = \frac{9}{3} = 3 \text{ m} \]

4. **Calculate the Velocity of the Wave**:
The velocity \(v\) of the wave can be calculated using the formula:
\[ v = f \cdot \lambda \]
Where \(f\) is the frequency. Given \(f = 120 \text{ Hz}\) and \(\lambda = 3 \text{ m}\):
\[ v = 120 \cdot 3 = 360 \text{ m/s} \]

### Final Answer:
The velocity of the wave is \(360 \text{ m/s}\).

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