Question

A sinusoidal wave travelling in the positive x-direction has an amplitude of `15.0 cm`, a wavelength of `40.0 cm` and a frequency of `8.00 Hz. The vertical displacement of medium at t=0 and x=0 is also 15 cm as shown in figure.

(a) Find the angular wave number `k`, period `T`, angular frequency `omega` and speed `v` of the wave.
(b) Write a general expression for wave function.

Answer 1

(a) Wave number `k=(2pi)/lambda=(2pi rad)/(40 cm) =pi/(20) rad//cm`
Time period `(T)=(1)/(f)=(1)/(8) s`
Angular frequency `omega=2pif=16pi rad//s`
speed of wave `v=flambda=320 cm//s`
(b) it is given that `A=15 cm`
and also `y=15 cm` at `x=0` and `t=0`
then using `y=A sin(omegat-kx+phi)`
`15=15 sinphi rArr sin phi=(1)`
or `phi(pi)/(2) rad`
therefore,the wave function is
`y=A sin (omegat -kx+(pi)/(2))`
`=(15 cm)sin[(16pirad s^(-1))t-((pi)/(20)(rad)/(cm))x+(pi)/(2)]`