Two waves are given by `y_(1)=asin(omegat-kx)` and `y_(2)=a cos(omegat-kx)`. The phase difference between the two waves is -

Options

A. `pi//4`
B. `pi`
C. `pi//8`
D. `pi//2`

Explanation

To find the phase difference between the two waves given by the equations \(y_1 = A \sin(\omega t - kx)\) and \(y_2 = A \cos(\omega t - kx)\), we can follow these steps:

### Step 1: Rewrite the cosine function in terms of sine
We know that the cosine function can be expressed in terms of sine using the identity:
\[ \cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right) \]
Using this identity, we can rewrite \(y_2\):
\[ y_2 = A \cos(\omega t - kx) = A \sin\left(\left(\omega t - kx\right) + \frac{\pi}{2}\right) \]

### Step 2: Identify the phase of each wave
Now we can identify the phases of both waves:
- For \(y_1\), the phase is \(\phi_1 = \omega t - kx\).
- For \(y_2\), the phase is \(\phi_2 = \left(\omega t - kx\right) + \frac{\pi}{2}\).

### Step 3: Calculate the phase difference
The phase difference \(\Delta \phi\) between the two waves is given by:
\[ \Delta \phi = \phi_2 - \phi_1 \]
Substituting the expressions for \(\phi_1\) and \(\phi_2\):
\[ \Delta \phi = \left(\left(\omega t - kx\right) + \frac{\pi}{2}\right) - \left(\omega t - kx\right) \]
This simplifies to:
\[ \Delta \phi = \frac{\pi}{2} \]

### Conclusion
Thus, the phase difference between the two waves is:
\[ \Delta \phi = \frac{\pi}{2} \]

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