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 ?

A wave travels along the positive x-direction with a speed of `20 ms^-

1.	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» Correct Answer - A::B::C::D 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`

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