Two waves ${y_1} = {A_1}\sin (\omega t - {\beta _1})$, ${y_2} = {A_2}\sin (\omega t - {\beta _2})$ Superimpose to form a resultant wave whose amplitude is
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(a) Phase difference between the two waves is
$\phi = (\omega t - {\beta _2}) - (\omega t - {\beta _1}) = ({\beta _1} - {\beta _2})$
Resultant amplitude $A = \sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos ({\beta _1} - {\beta _2})} $
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