A progressive wave of frequency 50 Hz is travelling with a velocity of 350 m/s. through a medium. What is the change in phase at a given place in time interval of 0.01 second ?

Options

A. `(pi)/(4)` radian
B. `(pi)/(2)` radian
C. `pi` radian
D. `(3pi)/(2)` radian

Explanation

To solve the problem, we need to find the change in phase of a progressive wave over a given time interval. We can use the relationship between frequency, angular frequency, and phase change.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Frequency (f) = 50 Hz
- Velocity (v) = 350 m/s
- Time interval (Δt) = 0.01 s

2. **Calculate Angular Frequency (ω):**
The angular frequency (ω) is related to the frequency (f) by the formula:
\[ \omega = 2\pi f \]
Substituting the given frequency:
\[ \omega = 2\pi \times 50 = 100\pi \, \text{rad/s} \]

3. **Calculate Change in Phase (Δφ):**
The change in phase (Δφ) over a time interval (Δt) can be calculated using the formula:
\[ \Delta \phi = \omega \Delta t \]
Substituting the values of ω and Δt:
\[ \Delta \phi = (100\pi) \times 0.01 = \pi \, \text{radians} \]

4. **Final Result:**
The change in phase at a given place in a time interval of 0.01 seconds is:
\[ \Delta \phi = \pi \, \text{radians} \]