One end of a long string of linear mass density `8.0 xx 10^(-3) kg m^(-1)` is connected to an electrically driven tuning fork of frequency 256Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t=0, the left end (fork end) of the string x=0 has zero transverse displacement (y=0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.

Explanation

(i) Wave velociy,
`v = sqrt ((T)/(mu)) = sqrt (( mg )/(mu))= sqrt (( 90 xx 9.8)/(8 xx 10 ^(-3)))=332 (m)/(s)`
`(ii) omega = 2pi f = 2 xx 3.14 xx 256 = 1608 rad//s`
(iii)` v = (omega )/(k) implies k = (omega )/(v) = (1608)/(332) =4.843 (rad)/(s)`
(iv) Required equation `y = a sin (omega t -kx)`
`therefore y =0.05 sin (1608 t -4.843 )m`