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.
Related questions
If a source emits sound of frequency 500 Hz and moves at 20 m/s toward a stationary observNewton's formula for the speed of sound in air (assuming isothermal process) predicted a vFor a longitudinal wave in air, the excess pressure and displacement are related such thatThe wave equation y = 0.05 sin(20πx − 100πt) SI units. The wave speed isThe fundamental frequency of a vibrating string of length L, tension T, linear density μ iTwo waves overlap to produce a standing wave on a string. The nodes are points whereThe speed of light in vacuum isWhen a wave is reflected from a rigid boundary (fixed end of a string), the reflected wave