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. `2pixx10^(-2)m`
B. `10^(-3)m`
C. `pixx10^(-3)m`
D. `2pixx10^(-3)m`

Answer

A

Explanation

Maximum speed of any point on the string `aomega=a(2pif)`
`therefore =(v)/(10)=(10)/(10)=1` (givenv=10jm/s)
`therefore 2piaf=1 implies f=(1)/(2pia)`
`a=10^(-3)m` (given)
`therefore f=(1)/(2pixx10^(-3))=(10^(3))/(2pi)Hz`

Speed of wave`v=flamda" "therefore (10m//s)=((10^(3))/(2pi)s^(-1))lamda`
`implies therefore lamda=2pixx10^(-2)m`