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

$\Delta \phi = \frac{2\pi}{\lambda}\Delta x$

now we will have

$2N\pi = \frac{2\pi}{\lambda}\Delta x$

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