Question

Two point sources are vibrating in phase producing two-dimensional water wave interference. The first antinodal line on either side of the central maximum will occur at locations where the path difference of the arriving waves is:

Question 9 options:

A)

1/4 λ

B)

1/2 λ

C)

3/4 λ

D)

λ

E)

2λ

Answer 1

For all antinodal positions we know that

`\Delta \phi = 2N\pi`

now we also know the relation between phase difference and path difference

`\Delta \phi = (2\pi)/(\lambda)\Delta x`

now we will have

`2N\pi = (2\pi)/(\lambda)\Delta x`

now from above equation we will have

`\Delta x = N\lambda`

now for the first anti node position

N = 1

`\Delta x = \lambda`

Option D is correct