Let the two waves `y_(1) = A sin ( kx - omega t)` and `y_(2) = A sin ( kx + omega t)` from a standing wave on a string . Now if an additional phase difference of `phi` is created between two waves , then

Options

A. the standing wave will have a different frequency
B. the standing wave will have a different amplitude for a given point
C. the spacing between two consecutives nodes will change
D. None of the above

Answer

B

Explanation

Initially the standing wave equation is
` y = 2 A sin kx cos omega t`
If phase difference `phi` is added to one of waves , then resulting standing wave equation is
` y = 2 A ( kx + (phi)/(2)) cos ( omega t - (phi)/( 2))`
Here, frequency does not change and also spacing between two successive nodes not change as its value for both is `pi//k`. But for a particle , in standing wave , amplitude changes.