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A wave travelling along a string is desc...

A wave travelling along a string is described by, `y(x, t) = 0.005 "sin" (80.0 x – 3.0 t)`, in which the numerical constants are in SI units `(0.005 m, 80.0 "rad" m^(-1)`, and `3.0 "rad" s^(-1))`. Calculate (a) the amplitude, (b) the wavelength, and (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

On comparing this displacement equation with, `y(x,y)=asin(kx-omegat)`
(i) The amplitude of the wave is 0.005m=5mm.
The angular wave number k and angular frequency `omega` are `k=80.0m^(-1) and omega=3.0s^(-1)`
we then relate the wavelength `lamda` to k through `lamda=2pi//k=7.85cm`
(iii) Now we relate T to `omega` by the relation `T=2pi//Omega=2.09s` and frequency `v=1//T=0.48Hz`.
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