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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 cmat =0.8 s? |
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Answer» <P> Solution :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` |
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