Question

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.​

Answer 1

Answer:

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Answer 2

v = ω/k

Comparing with general formula of sinusoidal waves, ω = 314/s, k = 157/m

Thus, v = 2 m/s

$y = 20sin(157x)cos(314t)\\y = 10[2sin(157x)cos(314t)]\\y = 10[sin(157x + 314t) + sin(157x - 314t)]\\y = 10sin(157x + 314t) + 10sin(157x - 314t)$

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