Two waves Y₁=A₁ sin ,(omega t -β₁) and Y₂ = A₂ sin ,(omega t -β₂) superimpose to

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14.Waves and Sound

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Two waves $Y_1=A_1 \sin \,(\omega t -\beta_1)$ and $Y_2 = A_2 \sin \,(\omega t -\beta_2)$ superimpose to form a resultant wave whose amplitude is

A

$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\,\cos \,({\beta _1} - {\beta _2})} $

B

$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\,\sin \,({\beta _1} - {\beta _2})} $

C

$A_1 + A_2$

D

$(A_1 + A_2)$

Solution

Phase difference between the superimposing waves is $\left(\beta_{1}-\beta_{2}\right)$

Resultant amplitude

$=\sqrt{\mathrm{A}_{1}^{2}+\mathrm{A}_{2}^{2}+2 \mathrm{A}_{1} \mathrm{A}_{2} \cos \left(\beta_{1}-\beta_{2}\right)}$

Standard 11

Physics

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