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 `100ms^(-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 wavelength`(s)` of these sationary waves is (are)

Options

A. `y(t)=Asin((pix)/(6))cos((50pit)/(3))`
B. `y(t)=Asin((pix)/(3))cos((100pit)/(3))`
C. `y(t)=Asin((5pix)/(6))cos((250pit)/(3))`
D. `y(t)=Asin((5pix)/(6))cos250pit`

Answer

A, C, D

Explanation

There will be a node at `x=0` and antinode at `x=3` .Here, `upsilon=(omega)/(k)=100m//s.`
Hence, at `x=0,y=0`
and at`x=3cm,y=+A.`
The above conditions are satisfied in options (a), (c) and (d).