In a stationary wave represented by `y = a sin omegat cos kx`, amplitude of the component progerssive wave is

Options

A. `(a)/(2)`
B. `a`
C. `2a`
D. None of these

Explanation

To find the amplitude of the component progressive wave in the stationary wave represented by the equation \( y = a \sin(\omega t) \cos(kx) \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given equation**: The stationary wave is given by the equation \( y = a \sin(\omega t) \cos(kx) \). Here, \( a \) is the amplitude of the stationary wave.

2. **Use the trigonometric identity**: We can use the trigonometric identity for the product of sine and cosine:
\[ \sin A \cos B = \frac{1}{2} [\sin(A + B) + \sin(A - B)] \]
In our case, let \( A = \omega t \) and \( B = kx \).

3. **Rewrite the equation**: Applying the identity, we can rewrite the stationary wave equation:
\[ y = a \sin(\omega t) \cos(kx) = \frac{a}{2} [\sin(\omega t + kx) + \sin(\omega t - kx)] \]

4. **Identify the progressive waves**: The terms \( \sin(\omega t + kx) \) and \( \sin(\omega t - kx) \) represent two progressive waves traveling in opposite directions.

5. **Determine the amplitude of the progressive waves**: The amplitude of each of these progressive waves is given by the coefficient in front of the sine functions. Since we have:
\[ y = \frac{a}{2} \sin(\omega t + kx) + \frac{a}{2} \sin(\omega t - kx) \]
The amplitude of each component progressive wave is \( \frac{a}{2} \).

6. **Conclusion**: Therefore, the amplitude of the component progressive wave is \( \frac{a}{2} \).

### Final Answer:
The amplitude of the component progressive wave is \( \frac{a}{2} \).