If $y_1=A\sin(\omega t-kx)$ and $y_2=A\sin(\omega t+kx)$ are superposed, the resultant displacement is
A$y=2A\sin\omega t\sin kx$
B$y=2A\cos\omega t\cos kx$
C$y=2A\sin\omega t\cos kx$
D$y=A\sin\omega t$
Answer & Solution
Correct answer: C. $y=2A\sin\omega t\cos kx$
Using $\sin C+\sin D=2\sin\frac{C+D}{2}\cos\frac{C-D}{2}$, with $C=\omega t-kx$ and $D=\omega t+kx$, we get $$y=2A\sin\omega t\cos kx.$$ This is the standard equation of a standing wave.
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