5) Displacement of a string in which a stationary wave is formed is given as
y = 20 sin 157 x Cos 314t where x is in cm and t is in seconds. Find (i) velocity of wave
(iii) Wavelength of individual waves.
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v = ω/k
Comparing with general formula of sinusoidal waves, ω = 314/s, k = 157/m
Thus, v = 2 m/s
Trigonometric identity: sin(x) + sin(y) = 2sin[(x+y)/2]cos[(x-y)/2]
So,
Individual wavelength λ = 2π/k
Thus, λ = 0.4 m for both waves
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