Halliday, Resnick & Walker — Waves-II: Problem 45

45 Figure 17-30 shows two point sources \( S_1 \) and \( S_2 \) that emit sound of wavelength \( \lambda = 3.00 \text{ m} \). The emissions are isotropic and in phase, and the separation between the sources is \( d = 16.0 \text{ m} \). At any point \( P \) on the \( x \) axis, the wave from \( S_1 \) and the wave from \( S_2 \) interfere. When \( P \) is very far away (\( x \approx \infty \)), what are (a) the phase difference between the arriving waves from \( S_1 \) and \( S_2 \) and (b) the type of interference they produce? Now move point \( P \) along the \( x \) axis toward \( S_1 \). (c) Does the phase difference between the waves increase or decrease? At what distance \( x \) do the waves have a phase difference of (d) \( 0.50\lambda \), (e) \( 1.00\lambda \), and (f) \( 1.50\lambda \)?