Which pair of equations can combine to produce a standing wave?
A$y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(\omega t+kx)$
B$y_1=A\sin(\omega t-kx)$ and $y_2=2A\sin(\omega t-kx)$
C$y_1=A\sin(\omega t-kx)$ and $y_2=A\cos(\omega t-kx)$
D$y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(2\omega t+kx)$
Answer & Solution
Correct answer: A. $y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(\omega t+kx)$
Standing waves require two waves with the same amplitude, same frequency, and same wave number moving in opposite directions. Only option A satisfies all these conditions; the others differ in amplitude, phase form without opposite propagation, or frequency.
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