A vibrating string is tied at its two ends. The equation of the wave produced on the string is given by `y= cos (2 pi t) sin (2pi x)`
What is the lenghts of the string,f it is in the fundamental node of vibration ?

Options

A. 1 m
B. `0.5 m`
C. `0.75 m`
D. `1.5 m`

Answer

B

Explanation

Since the string is fixed at its two ends, the wave produced on the string is a stationary wave.
Comparing the given equation ` y = cos (2 pi t) sin (2 pi x) ` with the standard equation
` y = 2A sin ((2pit)/T) cot ((2pix)/lambda)`,
We get ` (2pi x)/ lambda = 2 pi x :. lambda = 1 ` m
` :. ` For the fundamental mode , there is only are loop and
` l = lambda/2 = 1/2 ` m