The Total solution for NCERT class 6-12
One end of a long string of linear massdensity 8.0 × 10–3 kg m–1 is connected toan electrically driven tuning fork of frequency 256 Hz. The other end passesover a pulley and is tied to a pan containing a mass of 90 kg. The pulley endabsorbs all the incoming energy so that reflected waves at this end havenegligible amplitude. At t = 0, the left end (fork end) of thestring x = 0 has zero transverse displacement (y =0) and is moving along positive y-direction. The amplitude of thewave is 5.0 cm. Write down the transverse displacement y asfunction of x and t that describes the waveon the string.
The equation of a travelling wavepropagating along the positive y-direction is given by thedisplacement 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, m = 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 displacementequation:
y (x, t)= 0.05 sin (1.6 × 103t – 4.84 x)m