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

Options

A. `lamda = 2pi xx 10^(-2) m, n = 10^(3) Hz`
B. `lamda = 2pi m, n (10^(3))/(2pi) Hz`
C. `lamda = 2pi xx 10^(-2) m and n = (10^(3))/(2pi) Hz`
D. `lamda = pi xx 10^(-2) m and n = 10^(4) Hz`

Answer

C

Explanation

For the transverse wave `a = 10^(-3) m and v = 10 m//s`
The maximum particle velocity `v_("max") = aomega`
but `v_("max") = (v)/(10)`
`:. (v)/(10) = a. 2pin`
`:. (10)/(10) = 10^(-3) xx 2pi n " " :. 2pi n = 10^(3) or n = (10^(3))/(2pi)`
and `v = n lamda`
`:. lamda = (v)/(n) = (10)/(10^(3) //2pi) = 2pi xx 10^(-2) m`
Thus `lamda = 2pi xx 10^(-2) m and m = 10^(3)//2pi`