question_answer 11)

The transverse displacement of a string (clamped at its two ends) is given by                                           where x, y are m m and t in s. The length of the string is 1.5 m and its mass is 3 x  kg. Answer the following:                                                                                  (i) Does the function represent a travelling or a stationary wave ?                               (ii) Interpret the wave as a superimposition of two waves travelling in opposite directions. What are the wavelength, frequency and speed of propagation of each wave ?                             (iii) Determine the tension in the string.                                                       

Answer:

The given eqn. is    y (x, t)                   =    ??.(i) (i) As the equation involves harmonic functions of x and t separately, it represents a stationary wave. (ii) We know that when a wave pulse         travelling along + direction of x--axis is superimposed by the reflected wave travelling in opposite direction, a stationary wave is formed ?.(ii) Comparing (i) and (ii), we find that  or Also, or Frequency,  hertz Note that both the waves have same wave length, same frequency and same speed. (c) Velocity of transverse waves is        or where