Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180 $\circ$ .The resultant intensity is A)zero B)A C)A² D)2A² E)(3A)²

Question

Quizplus · Accepted Answer

The equation for the resultant intensity of two waves out of phase by 180 degrees is given by: I = I1 + I2 + 2√(I1*I2)*cos(Δφ) where I1 and I2 are the intensities of the two waves, Δφ is the phase difference between them. Here, I1 = A^2 and I2 = (2A)^2 = 4A^2 Thus, I = A^2 + 4A^2 + 2√(A^2 * 4A^2)*cos(180°) I = 5A^2 - 2A^2 = 3A^2 Therefore, the resultant intensity is 3A^2 or A² (option C).

Two Waves,one with Amplitude a and the Second with Amplitude ∘\circ∘

Two Waves,one with Amplitude a and the Second with Amplitude $\circ$