Question

The oscillations of two points x1 &x2 at x=0 &x=1 m respectively are modelled as follows ;
Y1 = .3 sin4pi t
Y2= .3 sin(4pi t +pi/8 )
Calculate the wave length And speed of the associated wave.

Answer 1

A progressive transverse wave (propagating in negative x direction) is modeled as            y(t, x) = A Sin (ωt  + k x)

So   y(t, x=0) = A Sin ωt ,    Given  y1(t,x1=0) =  0.3 Sin 4π t   meters
    Comparing these we get:   A = 0.3 m,   ω = 4π rad/s
        f = ω/2π = 2 Hz

Now  y(t, x=1m) = A Sin (ωt + k),   given  y2(t, x2=1m) = 0.3 Sin(4πt+π/8)
    compare them.   A = 0.3 m, ω = 4π rad/s,  f = 2Hz,  k = π/8  m⁻¹
            λ = wavelength = 2π/λ = 16 m
   speed of wave = f λ = 32 m/s