A progressive wave moves with a velocity of `36` m/s in a medium with a freqency of `200 Hz`. The phase difference between two particles separeted by a distance of `1 cm` is

Options

A. `40^(@)`
B. `20rad`
C. `(pi)/(9)` rad
D. `((pi)/(9))^(@)`

Explanation

To find the phase difference between two particles separated by a distance of 1 cm in a progressive wave, we can follow these steps:

### Step 1: Identify the given values
- Velocity of the wave, \( v = 36 \, \text{m/s} \)
- Frequency of the wave, \( f = 200 \, \text{Hz} \)
- Distance between the two particles, \( \Delta x = 1 \, \text{cm} = 0.01 \, \text{m} \)

### Step 2: Calculate the wavelength (\( \lambda \))
Using the wave equation:
\[ v = f \lambda \]
We can rearrange this to find the wavelength:
\[ \lambda = \frac{v}{f} \]
Substituting the values:
\[ \lambda = \frac{36 \, \text{m/s}}{200 \, \text{Hz}} = 0.18 \, \text{m} \]

### Step 3: Use the formula for phase difference (\( \Delta \phi \))
The phase difference between two points in a wave is given by:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
Substituting the values we have:
\[ \Delta \phi = \frac{2\pi}{0.18} \times 0.01 \]

### Step 4: Calculate \( \Delta \phi \)
Calculating the phase difference:
\[ \Delta \phi = \frac{2\pi \times 0.01}{0.18} \]
\[ \Delta \phi = \frac{0.02\pi}{0.18} = \frac{\pi}{9} \, \text{radians} \]

### Final Answer
The phase difference between the two particles separated by a distance of 1 cm is:
\[ \Delta \phi = \frac{\pi}{9} \, \text{radians} \]

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