A source oscillates with a frequency `25 Hz` and the wave propagates with `300m//s`. Two points `A` and `B` are located at distances `10m and 16m` away from the source. The phase difference between `A and B` is

Options

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

Explanation

To find the phase difference between points A and B, we can follow these steps:

### Step 1: Identify the given values
- Frequency (f) = 25 Hz
- Wave speed (v) = 300 m/s
- Distance from source to point A (x_A) = 10 m
- Distance from source to point B (x_B) = 16 m

### Step 2: Calculate the wavelength (λ)
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
Substituting the values:
\[ \lambda = \frac{300 \, \text{m/s}}{25 \, \text{Hz}} = 12 \, \text{m} \]

### Step 3: Calculate the path difference (Δx)
The path difference (Δx) between points A and B is given by:
\[ \Delta x = x_B - x_A \]
Substituting the values:
\[ \Delta x = 16 \, \text{m} - 10 \, \text{m} = 6 \, \text{m} \]

### Step 4: Calculate the phase difference (Δφ)
The phase difference (Δφ) can be calculated using the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
Substituting the values we have:
\[ \Delta \phi = \frac{2\pi}{12 \, \text{m}} \times 6 \, \text{m} \]
This simplifies to:
\[ \Delta \phi = \frac{2\pi \times 6}{12} = \pi \]

### Final Answer
The phase difference between points A and B is:
\[ \Delta \phi = \pi \, \text{radians} \]

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