A wave travels along the positive x-direction with a speed of `20 ms^-1`. The amplitude of the wave is 0.20 cm and the wavelength 2.0 cm. (a) Write a suitable wave equation which describes this wave. (b) What is the displacement and velocity of the particle at x = 2.0 cm at time t = 0 according to the wave equation written ? Can you get different values of this quantity if the wave equation is written in a different fashion ?

Answer

A, B, C, D

Explanation

Wave speed v=20 m/s
`A=0.20 cm`
`:. K=(2pi)/lamda=(2pi)/2=picm^-1`
`T=lamda/v=2/2000`
`=1/1000 se =10^-3sec`
`omega=(2pi)/T`
`=2pixx10^3sec^-1`
So, the wave equation is
`:. Y=(0.2cm)sin`
`[(picm^-1)x(2pixx10^-3sec^-1)]`
b. At `x=2cm and t=0,
y=(0.2)cmsin(pi)=0`
`:. v=romegacospix`
`=0.2x2000pixxcos2pi`
`=400pi`
`=400picm/s=4pim/s`