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 verticle displacement of the medium at `t = 0 and x = 0` is also `15.0 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

Correct Answer - A::B::C::D
(a) `k = (2pi)/(lambda) = (2pi)/(40) = 0.157 rad//cm`
`T = (1)/(f) = (1)/(8) =0.125 s`
`omega =(2pi)/(T) =(2pi)/(0.215) = 50.3 rad//s`
`v = (omega)/(k) = 320 cm//s`
(b) Amplitude is `15 cm`.
At `t = 0 , x = 0, y = + A`. Hence, equation should be a `cos` equation. Further, wave is travelling in positive x-direction. Hence, `omegat` and `kx` should have opposite signs.