The phase difference between two points separated by 1m in a wave of frequency 120 Hz is `90^(@)` . The wave velocity is

Options

A. 180 m/s
B. 240 m/s
C. 480 m/s
D. 720 m/s

Answer

To find the wave velocity given the phase difference and frequency, we can follow these steps:

### Step-by-step Solution:

1. **Identify Given Data**:
- Frequency (f) = 120 Hz
- Phase difference (φ) = 90° = π/2 radians
- Distance (d) = 1 m

2. **Use the Relationship Between Phase Difference and Path Difference**:
The relationship between phase difference (φ) and path difference (Δx) is given by:
\[ \Delta x = \frac{\lambda}{2\pi} \cdot \phi \]
Here, Δx is the path difference, λ is the wavelength, and φ is the phase difference in radians.

3. **Substitute the Known Values**:
Since the path difference (Δx) is given as 1 m, we can substitute the values into the equation:
\[ 1 = \frac{\lambda}{2\pi} \cdot \frac{\pi}{2} \]

4. **Simplify the Equation**:
Simplifying the equation gives:
\[ 1 = \frac{\lambda}{4} \]
Therefore, we can solve for λ:
\[ \lambda = 4 \text{ m} \]

5. **Calculate Wave Velocity (V)**:
The wave velocity (V) can be calculated using the formula:
\[ V = f \cdot \lambda \]
Substituting the known values:
\[ V = 120 \text{ Hz} \cdot 4 \text{ m} = 480 \text{ m/s} \]

6. **Final Answer**:
The wave velocity is:
\[ V = 480 \text{ m/s} \]

### Summary:
The wave velocity is 480 m/s.

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