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

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

100m{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 $y\left(t\right) = Asin \dfrac{\pix}{6}cos \dfrac{50\pit}{3}$
B $y\left(t\right) = Asin \dfrac{\pix}{3}cos \dfrac{100\pit}{3}$
C $y\left(t\right) = Asin \dfrac{5\pix}{6}cos \dfrac{250\pit}{3}$
D $y\left(t\right) = Asin \dfrac{5\pix}{2}\cos 250\pit$

Correct answer

A. $y\left(t\right) = Asin \dfrac{\pix}{6}cos \dfrac{50\pit}{3}$

Step-by-step solution

Taking

y ( t ) = Af ( 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,

{v}_{fundamental} = \dfrac{v}{4l} = \dfrac{25}{3}Hz

The correct option are A, C, D.

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