Two waves of equal frequency `f` and velocity `v` travel in opposite directions along the same path. The waves have amplitudes `A` and `3 A` . Then:

Options

A. the amplitude of the resulting wave varies with position between maxima of amplitude `4 A` and minima of zero amplitude.
B. the distance between a maxima and adjacent minima of amplitudes is `v//2f`
C. maximum amplitude is `4 A` and minimum amplitude is ` 2A`
D. The position of a maxima or minima of amplitude does not change with time

Answer

C, D

Explanation

`y = y_(1) + y_(2)`
` = A sin (omega t - kx) + 3 A sin(omega t + kx)`
`= A sin omega t cos kx - A cos omega t sin kx + 3 A sin omega t cos kx + 3 A cos omega t sin kx`
` = 4 A sin omega t cos kx + 2 A cos omega t sin kx`
` = 2 A sin omega t cos k x + 2 A sin (omega t + kx)`
It is combination of a stationary and travelling wave.
Maximum amplitude `= 4 A`
Minimum amplitude ` = 2 A`
Distance between points having amplitude ` 4 A` and `2 A` will be ` = lambda//4 = v//4 f`