The wave-function for a certain standing wave on a string fixed at both ends is `y(x,t) = 0.5 sin (0.025pix) cos500t` where `x` and `y` are in centimeters and `t` is seconds. The shortest possible length of the string is :

Options

A. `126 cm`
B. `160 cm`
C. `40 cm`
D. `80 cm`

Answer

C

Explanation

`K = 0.025 pi = (2pi)/(lambda) lambda = (2cm)/(0.025)`
Required length `= (lambda)/(2) = (1)/(0.025) = 40 cm`