One end of a long string of linear mass density 8.0×10-3 kgm-1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. 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 a function of x and t that describes the wave on the string.
The equation of a travelling wave propagating along the positive 
x-direction is given by:
 yx, t=asinωt  kx ....i
It is given in the question that:
Linear mass density, μ=8.0×10-3 kg m-1
Frequency of the tuning fork, ν=256 Hz
Amplitude of the wave, a=5.0 cm=0.05 m ....ii 
Mass of the pan, m = 90 kg 
Tension in the string, T = mg = 90 × 9.8 = 882 N
The velocity of the transverse wave v,
Angular frequency,
ω=2πν=2×3.14×256=1608.5=1.6×103rad/s         ...iii
Wavelength is given by,  λ=vv=332256m
Propagation constant is given by,
k=2πλ=2×3.14332256=4.84 m1              ...iv 
Substituting the values from equations ii, iii, and iv in equation i,
yx, t=0.05 sin1.6×103t4.84x m