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?

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