question_answer 24)

One end of a long string of linear mass density  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 ( = 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 = 0).y as function of x and t that describes the wave on the string.  

Answer:

Here, m = 8.0 x  kg m-1, v = 256 Hz, T = 90 kg = 90 x 9.8 = 882 N Amplitude of wave, r = 5.0 cm = 0.05 m. As, the wave propagating along the string is a transverse travelling wave, the velocity of the wave is given by         Propagation constant, As, the wave is propagating along positive x direction, the equation of the wave is Here, x, y are in metre and t is in second.