Question

The equation of a progressive wave travelling along the x axis is given by $y = 10 sin pi (2t - 0.01x)$ where y and x are in m and t in s.Calculate:(i) amplitude(ii) frequency and wavelength(iii) wave velocity.

Answer 1

y = 10 Sin π (2 t - 0.01 x)
   = 10 Sin (2π t - 0.01 π x)
   = A Sin (ω t - k x )

Amplitude = 10 meters.
Frequency = ω / 2π = f = 1 Hz
k = wave number = 0.01 π  rad/meter
   = 2π/λ
λ = 200 meters

Wavelength =  λ = 200 meters

wave velocity = v = λ f  = 200 m/sec