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A transverse wave of wavelength 50 cm is...

A transverse wave of wavelength 50 cm is travelling towards+vex-axis along a string whose linear density is `0.05 g//cm`. The tension in the string is 450 N. At t=0,the particle at x=0 is passing through its mean position wave. The amplitude of the wave is 2.5 cm.

Text Solution

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Let the wave be described by:
`y x,t Asinomegax-omegat phi_(0)omega and A=2.5 cm`
where `k=(2pi)/(lambda)=(2pi)/(0.5)=4pi`
`y(0,0)=0implies A sin phi_(0)=0`
`phi_(0) 0,pi`
we also have
`(dy/dt)_(0.0)lt0rArr -Aomega cosphi_(0)gt0`
From Eqs.(i) and (ii), we get `phi_(0) pi`
Velocity of transverse wave in the string is given by
`sqrt(T)/(mu)=sqrt(450)/(0.05xx10^(-1))=300 m//s`
`implies omega=2pi f=(2pic)/(lambda)=(pi(300))/(0.5)=1200pi rad//s`
using all the quntities, the equation is
`y 2.5sin4pix-1200pit pi cm`
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