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Two waves are simultaneously passing through a string and their equations are:

$y_{1} = A_{1} s i n k (x - v t), y_{2} = A_{2} s i n k (x - v t + x_{0}) .$ Given amplitudes A₁ = 12mm and A₂ = 5mm, x₀ = 3.5 cm and wave number k = 6.28 cm^-1. The amplitude of resulting wave will be________mm.

2 Views | Posted 3 months ago

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Answered by

alok kumar singh | Contributor-Level 10

3 months ago

Phase difference between the two waves,

$? = k x_{0} = 6.28 \times 3.5 = 7 π r a d$

Amplitude of resulting wave,

$A = \sqrt[]{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} c o s ?}$

$= \sqrt[]{1 2^{2} + 5^{2} + 2 \times 12 \times 5 \times c o s (7 π)}$

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