Two waves $y_1 = A_1\sin (ωt - β_1)$ and $y_2 = A_2 \sin (ωt - β_2)$ superimpose to form a resultant wave. The amplitude of this resultant wave is given by
Answer & explanation
Correct answer: option 3
Phase diff = $ωt - β_1-ωt - β_2=β_2-β_1$
∴ Amplitude of resultant wave
$=\sqrt{A_1^2+A_2^2+2A_1A_2\cos(β_2-β_1)}$
$=\sqrt{A_1^2+A_2^2+2A_1A_2\cos(β_1-β_2)}$ [As $\cos(-θ)=+\cos θ$]