Two coherent sources of water waves of frequency \(f\) and speed \(c\) are a distance \(d\) apart and equal in amplitude. Nodal lines exist where the path lengths from the sources differ by an odd number of half wavelengths (where the contributions are \(180^{\circ}\) out of phase).

(a) Far from the sources (where we can treat wavefronts from each source as parallel), what are the angles between the nodal lines in the water and the perpendicular to the line joining the sources?

(b) If you introduce a phase difference \(\phi\) between the sources, how do the directions of the nodal lines shift?