Question

The equation of a stationary wave is given by y (x, t)=2 sin pie x cos 100 pie t. where x and y are measured in metre and t in second. Calculate the amplitude, wavelength and frequency of component waves whose superposition generated this stationary wave. Also write the equations of component waves.

Answer 1

y(x, t) = 2 Sin 2π x   Cos 100π t
         = Sin (2πx + 100π t) + Sin (2πx - 100π t)

component waves are :
 y(x, t) Sin(2πx + 100π t) :  f = 100π/2π = 50 Hz,  Amplitude = 1 meter. 
                 k = 2π       λ = 2π/k  = 1 meter
   wave is traveling in negative x direction

y(x,t) = Sin(2πx - 100πt) :  f = 50 Hz,  Amplitude = 1m    k = 2π      λ = 1 m
         traveling in positive x direction.