A wave of frequency 20 Hz is propagatinig is space with speed 200 m/s. the phase difference of the two points of wave separated by a distance 5 m is

Options

A. `2pi` radian
B. `pi` radian
C. `(pi)/(3)` radian
D. `(pi)/(2)` radian

Answer

To find the phase difference between two points of a wave separated by a distance of 5 m, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data**:
- Frequency (f) = 20 Hz
- Speed of wave (v) = 200 m/s
- Distance (d) = 5 m

2. **Calculate Wavelength (λ)**:
- Use the wave equation:
\[ v = f \cdot \lambda \]
- Rearranging gives:
\[ \lambda = \frac{v}{f} \]
- Substitute the values:
\[ \lambda = \frac{200 \, \text{m/s}}{20 \, \text{Hz}} = 10 \, \text{m} \]

3. **Calculate Phase Difference (Δφ)**:
- The formula for phase difference is:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot d \]
- Substitute the values:
\[ \Delta \phi = \frac{2\pi}{10 \, \text{m}} \cdot 5 \, \text{m} \]
- Simplifying gives:
\[ \Delta \phi = \frac{2\pi \cdot 5}{10} = \pi \, \text{radians} \]

4. **Conclusion**:
- The phase difference between the two points separated by a distance of 5 m is \( \pi \) radians.

### Final Answer:
The phase difference is \( \pi \) radians.

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