Answer to Question #72636 in Mechanics | Relativity for Santhosh

Question

a) A sinusoidal wave is described by
y(x, t) = 3.0 sin (5.95t − 4.20x) cm
where x is the position along the wave propagation. Determine the amplitude, wave
number, wavelength, frequency and velocity of the wave. (2×5=10)
b) Two waves, travelling along the same direction, are given by
y1(x, t) = asin (w1t − k1x)
and y2 (x, t) = asin (w2t − k2x)

Answer 1

General form of a sinusoidal wave is
y(x,t)= A sin⁡(ωt -kx)
Where A is the amplitude, ω is the angular frequency, k is a wave number.
Thus:
Amplitude A=3.00 cm=0.03 m
Wave number k=4.20 m^(-1)
Wavelength λ=2π/k=2π/4.20=1.50 m
Frequency f=ω/2π=5.95/2π=0.95Hz
Velocity v=fλ=ω/k=5.95/4.20=1.42 m/s