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 of the wave. If `a = 10^(-3)m` and `v = 10ms^(-1)`, then `lambda` and `f` are given by

Options

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

Answer

A, C

Explanation

Maximum speed of any point on the string `= a omega`
`:. =(v)/(10)=(10)/(10)=1("Given" = v =10m//s)`
`:. 2piaf=1`
`:. f=(1)/(2pia) rArr a = 10^(-3) m` (Given)
`:. f=(1)/(2pixx10^(-3))=(10^(3))/(2pi)Hz`
Speed of wave `= f lamda`
`:.(10m//s)=((10^(3))/(2pi)s^(-1))lamda`
`:. lamda =2pixx10^(-2)m`.