Question

The equation of a progressive wave is y = 0.50 sin (500 t - 0.025x), where y, t and x are in cm, second and metre. Calculate

(i) amplitude
(ii) angular frequency
(iii) period
(iv) wavelength and
(v) speed of propagation of wave.

Answer 1

equation of wave y = 0.50 sin(500t-0.025x)
compare with y = A sin(wt - kx)
A = 0.50 cm.                                      (amplitude)
w = 500 sec^-1
w = 2pi/T                                           (angular frequency)
T = pi/250 sec.                                   (period)
lambda = 2pi/k
           = 2pi/0.025
           = 80pi  metre                          (wavelength)
v = w/k = 500/0.025
     = 2*10^4 m/sec                            (speed of propagation of wave)