A transverse wave given by `y = 2 sin (0.01 x + 30t)` moves on a strected string from one end to another end in 0.5 sec. If x and y are in cm and t is in sec, then the length of the string is

Options

A. 6 m
B. 9 m
C. 12 m
D. 15 m

Answer

D

Explanation

`y = 2 sin (30 t + (x)/(100))`
`= 2 sin 2pi ((30t)/(2pi) + (x)/(2pi (100)))`
Comparing with `y = A sin 2pi ((t)/(T) + (x)/(lamda))`
we get, `T = (2pi)/(30) :. n = (30)/(2pi) and lamda = 2pi (100)`
`:. v = n lamda = (30)/(2pi) xx 2pi (100) = 30 m//s`
`:' v = (l)/(t) :.` length of the string `= 30 xx 0.5 = 15m`