question_answer 22)

A travelling harmonic wave on a string is described by y (x, t) = 7.5 sin (0.0050 x + 121 + /4) (a) what are the displacement and velocity of oscillation of a point at x = 1 cm, and ( = 1 s ? Is this velocity equal to the velocity of wave propagation ? (b) Locate the points of the string which have the same transverse displacement and velocity as the x = 1 cm point at (= 2 s, 5 s and 11 s.  

Answer:

The travelling harmonic wave is y (x, t) = 7.5 sin (0.0050 x + 12 t + /4) At x = 1 cm and t = 1 sec,     ?..(i) Now,  radian            degree                               from (i),                                                                                   velocity of oscillation,                                                 At, x = 1 cm, t = 1 sec.                                                             Comparing the given eqn. with the standard form     We get,  or velocity of wave propagation, We find that velocity at x = 1 cm t = 1 sec is not equal to velocity of wave propagation.               (b) Now, all points which are at a distance ofK from x = 1 cm will have same transverse displacement and velocity. As therefore, all points at distances ... from x = 1 cm will have same displacement and velocity, as x = 1 cm point at t = 2 s, 5 s and 11 s.