Wave represented by the equation \( y_1 = A \cos(kx - \omega t) \) is superimposed on another wave to form a stationary wave such that the point \( x = 0 \) is a node. The equation representing the wave is given by
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- \( A \cos(kx + \omega t) \)
- \( -A \cos(kx + \omega t) \)
- \( A \sin(kx + \omega t) \)
- \( -A \sin(kx - \omega t) \)
The Correct Option is B
Solution and Explanation
When two waves interfere to form a stationary wave with a node at \( x = 0 \), the equation of the resulting wave can be obtained by adding the two individual waves. The general equation for a stationary wave is: \[ y = 2A \cos(kx) \cos(\omega t) \] Given the form of the wave \( y_1 = A \cos(kx - \omega t) \), for \( x = 0 \) to be a node, the second wave must have the opposite sign of the first, resulting in the equation \( -A \cos(kx + \omega t) \).
Hence, the correct answer is (b).
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