6. A progressive wave of amplitude a has intensity 1. This wave combines with another wave of amplitude 0.6a at a point in space. The phase difference between the waves is 180^circ What is the resultant intensity of the combined waves in terms of l?

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6. A progressive wave of amplitude a has intensity 1. This wave combines with another wave of amplitude 0.6a at a point in space. The phase difference between the waves is 180^circ What is the resultant intensity of the combined waves in terms of l?

Answer 1

The intensity of the interference of the two waves is \( 0.16I \).

Answer 2

## Step 1: Understanding the scenario We are looking at two progressive waves combining at a point in space. Since the phase difference between the two waves is \( 180^{\circ} \), we recognize that this is a case of destructive interference. ## Step 2: Calculating the resultant amplitude When waves interfere destructively, their amplitudes subtract. The existing wave has an amplitude of \( a \), while the newly introduced wave has an amplitude of \( 0.6a \). The resultant amplitude is therefore \( a - 0.6a = 0.4a \). ## Step 3: Relating intensity to amplitude Intensity of a wave is proportional to the square of its amplitude. ### **Therefore, if \( I \) is the intensity corresponding to the amplitude \( a \), intensity \( I_1 \) corresponding to the amplitude \( 0.4a \) can be calculated by \( I_1 = \Bigl(\frac{0.4a}{a}\Bigr)^2 \times I = 0.16I \).**

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6. A progressive wave of amplitude a has intensity 1. This wave combines with another wave of amplitude 0.6a at a point in space. The phase difference between the waves is 180^circ What is the resultant intensity of the combined waves in terms of l?

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