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One end of a long string of linear mass ...

One end of a long string of linear mass density `10^(-2) kg m^(-1)` is connected to an electrically driven tuning fork of frequency 150 Hz. The other end passes over a pulley and is tied to a pan containig a mass of 90 kg. the pulley end absorbs all the incoming energy so that reflected waves from this end have neglidible amplitude , At t =0, the left end (fork end ) of the string is at x=0 has a transverse displacement of 2.5 cm and is moving along positive y-direction. the amplitude of the wave is 5 cm. write down the transverse displacement y (in cetimetres) as function of x(in metres) and t (in seconds ) that describes the wave on the string.

Text Solution

Verified by Experts

`theta=pi//6`
`v=sqrt(T//mu)=sqrt(900)/(0.01)=300 m//s`
frequency `=150 Hz`
`:.lambda=(v)/(f)=(300)/(150)=2m`
Then equation will be
`y=A sin{2pi((t)/(T)-(x)/(lambda))+theta}`
`=5 sin{2pi(150t-(x)/(2))+(pi)/(6)}`
`=5 sin{pi(300t-x)+(pi)/(6)}`
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