The speed of a wave in a streched string is `20ms^(-1)` and its frequency is 50 Hz. Calculate the phase difference in radian between two points situated at a distance of 10 cm on the string.

Options

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

Answer

To solve the problem of finding the phase difference between two points on a stretched string, we can follow these steps:

### Step 1: Identify the given values
- Speed of the wave (v) = 20 m/s
- Frequency (f) = 50 Hz
- Distance between the two points (Δx) = 10 cm = 0.1 m

### Step 2: Calculate the wavelength (λ)
The wavelength can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
Substituting the known values:
\[ \lambda = \frac{20 \, \text{m/s}}{50 \, \text{Hz}} = \frac{20}{50} = 0.4 \, \text{m} \]

### Step 3: Use the formula for phase difference (Δφ)
The phase difference (Δφ) between two points separated by a distance Δx is given by the formula:
\[ \Delta \phi = \frac{2\pi \Delta x}{\lambda} \]
Substituting the values we have:
\[ \Delta \phi = \frac{2\pi \times 0.1 \, \text{m}}{0.4 \, \text{m}} \]

### Step 4: Simplify the expression
Calculating the right side:
\[ \Delta \phi = \frac{2\pi \times 0.1}{0.4} = \frac{2\pi \times 1}{4} = \frac{\pi}{2} \]

### Step 5: State the final answer
The phase difference between the two points situated at a distance of 10 cm on the string is:
\[ \Delta \phi = \frac{\pi}{2} \, \text{radians} \]

### Summary
The phase difference between the two points is \(\frac{\pi}{2}\) radians.

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