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One end of a taut string of length 3m along the x axis...

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string is 100 ms-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)
y(t)=Asinπx6cos50πt3
y(t)=A sinπx3cos100πt3
y(t)=Asin5πx6cos250 πt3
y(t)=Asin5πx2cos250 πt
Solution:
Taking y(t) = A f(x) g(t) & Applying the conditions:
1; here x = 3m is antinode & x = 0 is node
2; possible frequencies are odd multiple of fundamental frequency.
Where, vfundamental=v4l=253Hz
The correct option are A, C, D.