The frequencies of two sound sources are 256 Hz and 260 Hz, At `t=0` the intesinty of sound is maximum. Then the phase difference at the time `t=1//16` sec will be

Options

A. Zero
B. `pi`
C. `pi//2`
D. `pi//4`

Answer

To solve the problem, we need to find the phase difference between two sound sources with frequencies of 256 Hz and 260 Hz at a time of \( t = \frac{1}{16} \) seconds.

### Step-by-Step Solution:

1. **Identify the Beat Frequency**:
The beat frequency \( f_b \) is the difference between the two frequencies:
\[ f_b = f_2 - f_1 = 260 \text{ Hz} - 256 \text{ Hz} = 4 \text{ Hz} \]

2. **Calculate the Angular Frequency**:
The angular frequency \( \omega \) is related to the beat frequency by:
\[ \omega = 2\pi f_b = 2\pi \times 4 \text{ Hz} = 8\pi \text{ rad/s} \]

3. **Calculate the Phase Difference**:
The phase difference \( \Delta \phi \) at time \( t \) can be calculated using the formula:
\[ \Delta \phi = \omega \cdot t \]
Substituting the values we have:
\[ \Delta \phi = 8\pi \cdot \frac{1}{16} = \frac{8\pi}{16} = \frac{\pi}{2} \text{ radians} \]

4. **Final Answer**:
The phase difference at \( t = \frac{1}{16} \) seconds is:
\[ \Delta \phi = \frac{\pi}{2} \text{ radians} \]