3. A sinusoidal wave is described by the wave function: y = (0.25 m)cos(0.3x + 4

Question

3. A sinusoidal wave is described by the wave function:
          y = (0.25 m)cos(0.3x + 40t)
where x and y are in metres and t in seconds. Determine for this wave
the:
a. Amplitude
b. Angular frequency
c. Wavenumber
d. Wavelength
e. Wave speed
f. Direction of motion
g. Transverse velocity at t=5 s and x=2.0 m. 3. A sinusoidal wave is described by the wave function:
          y = (0.25 m)cos(0.3x + 40t)
y = (0.25 m)cos(0.3x + 40t) where x and y are in metres and t in seconds. Determine for this wave
the:
a. Amplitude
b. Angular frequency
c. Wavenumber
d. Wavelength
e. Wave speed
f. Direction of motion
g. Transverse velocity at t=5 s and x=2.0 m.

Explanation / Answer

Given Y = (0.25 m)cos(0.3x + 40t) compare this with y = A *cos(kx +wt) Here (a)A = 0.25 m (b)W = angular frequency = 40 cycles per sec (c) wave number = K = 0.3 (d) wave length lamda = 2*pi / K = 20.93 m (e) wave speed = v = w / k = 40 / 0.3 = 133.3 m/s (f) direction is along negative x direction (g)Transverse velocity = dy /dt = -(0.25)sin(0.3*2.0 +40*5) = 0.0875 m/s

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