The phase difference between the waves `y=acos(omegat+kx) and y=asin(omegat+kx+(pi)/(2))` is

Options

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

Answer

To find the phase difference between the two waves given by the equations \( y = a \cos(\omega t + kx) \) and \( y = a \sin(\omega t + kx + \frac{\pi}{2}) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Phase of Each Wave:**
- The first wave is given by \( y_1 = a \cos(\omega t + kx) \).
- The phase of this wave is \( \phi_1 = \omega t + kx \).
- The second wave is given by \( y_2 = a \sin(\omega t + kx + \frac{\pi}{2}) \).
- The phase of this wave is \( \phi_2 = \omega t + kx + \frac{\pi}{2} \).

2. **Calculate the Phase Difference:**
- The phase difference \( \Delta \phi \) between the two waves is given by:
\[ \Delta \phi = \phi_2 - \phi_1 \]
- Substituting the phases we found:
\[ \Delta \phi = \left( \omega t + kx + \frac{\pi}{2} \right) - \left( \omega t + kx \right) \]
- Simplifying this expression:
\[ \Delta \phi = \frac{\pi}{2} \]

3. **Conclusion:**
- The phase difference between the two waves is \( \frac{\pi}{2} \).

### Final Answer:
The phase difference between the waves \( y = a \cos(\omega t + kx) \) and \( y = a \sin(\omega t + kx + \frac{\pi}{2}) \) is \( \frac{\pi}{2} \).