The displacement of a standing wave on a string is given by yox, 1) = 0.4 sin (0.5.x) cos (300) where Xandy are in centimeters.
(a) Find the frequency, amplitude and wave speed of the component waves.
(b) What is the particle velocity `x=2.4 cm ` at =0.8 s?

Explanation

The given wave can be written as the sum of two component waves `y_(1)=0.2 sin (0.5x-30t) and y_(2)=0.2 sin (0.5x+30t)`
Now` omega=30(rad)/(s) and k=0.5 cm^(-1)`
`:.` Freqency of `f=(omega)/(2pi)=(15)/(pi)Hz`
amplitude `A=0.2 cm`
and were speed, `V=(omega)/(K)=(30)/(0.5)=60 cm//s`
(b) particle velocity
`v_(p)(x,t)=(dy)/(dt)=-12 sin (0.5x)sin(30t)`
`v_(p)(x=2.4 cmt,=0.8s)`
`=-12 sin(1.2 sin(24)=10.12 cm//s`