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

We use `k = (2pi)/(lambda) = 0.025 pi`
`(lambda)/(2) = (1)/(0.025) = 40 cm`
The shortest possible length will be `L_(min) = (lambda)/(2) = 40 cm`