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One end of a long string of linear mass density 8.0 × 10–3 kg m–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 function of x and t that describes the wave on the string.

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The equation of a travelling wave propagating along the positive y-direction is given by the displacement equation: y (x, t) = a sin (wt – kx) … (i) Linear mass density, Frequency of the tuning fork, ν = 256 Hz Amplitude of the wave, a = 5.0 cm = 0.05 m … (ii) Mass of the pan,...
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The equation of a travelling wave propagating along the positive y-direction is given by the displacement equation:

y (xt) = a sin (wt – kx) … (i)

Linear mass density, 

Frequency of the tuning fork, ν = 256 Hz

Amplitude of the wave, = 5.0 cm = 0.05 m … (ii)

Mass of the pan, = 90 kg

Tension in the string, T = mg = 90 × 9.8 = 882 N

The velocity of the transverse wave v, is given by the relation:

Substituting the values from equations (ii), (iii), and (iv) in equation (i), we get the displacement equation:

(xt) = 0.05 sin (1.6 × 103t – 4.84 x) m

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