A transverse sinusoidal wave of amplitude a, wavelength `lambda` and frequency `f` is travelling on a stretched string. The maximum speed of any point in the string is `v//10`, where `v` is the speed of propagation if the wave. If `a = 10^(-3)m` and `v = 10ms^(-1)`, then `lanbda` and `f` are given by

Options

A. (a) `lambda = 2pi xx 10^(-2)m`
B. (b) `lambda = 10^(-3)m`
C. ( c ) `f = 10^(3) Hz//(2pi)`
D. (d) `f = 10^(4)Hz`

Answer

A, C

Explanation

(a,c) NOTE : For a transverse sinusoidal wave travelling on a stirng, the maximum velocity is `aomega`.
But maximum velocity is `(v)/(10) = (10)/(10) = 1m//s`
:. `aomega = 1` rArr `10^(-3) xx 2piv = 1`
`v = (1)/(2pi xx 10^(-3)) = (10^(3))/(2pi) Hz`
:. `lambda = (v)/(v) = (10)/(10^(3)//2pi) = 2pi xx 10^(-2)m`