One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 m `s^(-1)`. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)

Options

A. `y(t) = A sin (pi x)/(6) cos (50 pi t)/(3)`
B. `y(t) = A sin (pi x)/(3) cos (100 pi t)/(3)`
C. `y (t) = A sin (5 pi x)/(6) cos (250 pi t)/(3)`
D. `y(t) = A sin (5 pi x)/(2) cos 250 pi t`

Answer

A, C, D

Explanation

At `{:(x=0 y=0),(x=3 y=0),((omega)/(k)=100 m//s):}]`
The equation satisfying all three conditions is correct.