Two harmonic travelling waves are described by the equations y 1 = a sin k x - ω t and y 2 = a sin - k x + ω t + ϕ The amplitude of the superposed wave is

Question

Two harmonic travelling waves are described by the equations y 1 = a sin k x - ω t and y 2 = a sin - k x + ω t + ϕ The amplitude of the superposed wave is, 2 a cos ϕ 2, 2 a sin ϕ, 2 a cos ϕ, 2 a sin ϕ 2

MARKS App · Accepted Answer

y 1 = a sin k x - ω t . . . 1 y 2 = a sin - k x + ω t + ϕ . . . 2 On adding 1 and 2 , y 1 + y 2 = 2 asin k x - ω t + - k x + ω t + ϕ 2 cos k x - ω t + k x - ω t - ϕ 2 = 2 asin ϕ 2 cos 2 ( k x + ω t ) - ϕ 2 Amplitude, A ϕ is a function of phase difference ϕ between constituent of waves ∴ ϕ = 2 a sin ϕ 2

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