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A wave travelling along a strong is desc...

A wave travelling along a strong is described by
`y(x,t)=0.005 sin (80.0x-3.0t)`
in which the numerical constants are in SI units `(0.005m, 80.0 rad m^(-1)` and `3.0 rad s^( -1))`. Calculate (a) the amplitude. (b) the wavelength (c) the period and frequency of the wave. Also , calculate the displacement y of the wave at a distance `x=30.0` cm and time t=20 s?

Text Solution

Verified by Experts

The given equation is
`y(x,t)=0.005sin[80.0x-3.0t]`
Comparing with the standard eqn.
`y(x,t)=rsin[(2pix)/(lambda)-(2pit)/(T)]`, we get
(i) `r=0.005m=5mm.` This is the amplitude.
(ii) `(2pi)/(lambda)=80.0, lambda=(2pi)/(80.0)=(pi)/(400)metre`
`=(pi)/(40)xx100cm=7.85cm`
(iii) `(2pi)/(T)=3.0,T=(2pi)/(3.0)=(2xx22)/(3xx7)=2.09s,`
`v=(1)/(T)=(1)/(2.09)=0.48Hz`
(iv) At, `x=30.0cm and t=20s,`
`y=0.005sin(80.0xx(30)/(100)-3.0xx20)`
`=0.005sin(24-60)=0.005sin(-36)`
`=0.005sin(-36+12pi)`
`=0.005sin(-36+37.71)`
`=0.005sin(1.71rad)`
`y=0.005sin(98.03^(@))=0.005xx1m`
`=5mm`
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