# Answer to Question #72636 in Mechanics | Relativity for Santhosh

Question #72636

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)

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)

Expert's answer

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

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

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