"Vibrators A and B are sources of waves with different wavelengths and they are placed close to one another in a ripple tank. Waves from source A have a wavelength of 8.0cm while those from B have a wavelength of 10cm. The waves start out in phase with each other. For each distance below, state whether the waves will experience constructive or destructive interference.

a) 20cm from both sources
b) 40cm from both sources
c) 80cm from A and 70cm from B
d) 40cm from A and 75cm from B"

I know what constructive and destructive interference are, but I don't know what to do in order to solve this question.

Calculate the number of waves between source and receiver for each case.

For case b), you are 5 wavelengths from A ande 4 wavelengths from B.

That would be a constructive interference situation.

Do the others similarly.

Thank you so much!

To determine whether the waves will experience constructive or destructive interference at different distances in this scenario, you can use the concept of path difference. The path difference is the difference in distances traveled by waves from two different sources to reach a particular point.

Here's how you can find out whether the waves will exhibit constructive or destructive interference at each distance:

a) For a point located 20 cm from both sources, calculate the path difference for the waves:
Path difference = distance from source A - distance from source B
= 20 cm - 20 cm = 0 cm

Since the path difference is zero, the waves will experience constructive interference. This means that the crests of the waves from both sources will align, resulting in a larger amplitude.

b) For a point located 40 cm from both sources:
Path difference = 40 cm - 40 cm = 0 cm

Similarly, since the path difference is zero, the waves will experience constructive interference.

c) For a point located 80 cm from source A and 70 cm from source B, calculate the path difference between the two sources:
Path difference = distance from source A - distance from source B
= 80 cm - 70 cm = 10 cm

The path difference here is not zero, but rather 10 cm. Since the path difference is half the wavelength of one of the sources' waves (8 cm/2 = 4 cm), the waves will undergo destructive interference. This means that the crest of one wave will align with the trough of the other wave, resulting in a cancellation of amplitudes.

d) For a point located 40 cm from source A and 75 cm from source B:
Path difference = distance from source A - distance from source B
= 40 cm - 75 cm = -35 cm

In this case, the path difference is negative, which indicates that the waves will experience destructive interference. The actual magnitude of the negative path difference does not affect the interference pattern—only the sign matters.

By analyzing the path differences, you can determine whether the waves will exhibit constructive or destructive interference at different distances from the sources.