HCI 10A Superposition Solutions (Self-Review Questions)

Hwa Chong Institution (College) C1 2023 1 Suggested Solutions Tutorial 10A : Superposition & Interference Self-Practice Questions: S1 This question tests students on application of Principle of Superposition. S2 This question tests students on understanding of phase difference and how it relates to destructive interference. At point P , waves from S 1 and S2 meet in antiphase at P (i.e. destructive interference) . Correct Option is A. 2a a a + = Sketching the graphs for S1 and S 2 may help you visualize the problem better. F This question is similar to Lecture Example 10.3.1. The strategy is to sketch the individual waveforms of each wave at any desired time, then add up their displacements.

Hwa Chong Institution (College) C1 2023 2 S3 (a) This question is a calculation question relating path difference to interference. Given that the pair of speakers (i.e. the sources) are driven by the same oscillator, this implies that the speakers are in phase. By applying Pythagoras Theorem, 22 1 22 2 1.15 8.00 8.082 1.85 8.00 8.211 rm rm = + = = + = Given that the first minimum occurs at P, this implies that Path difference = (r2 – r1) = /2 Solving, we get 0.258m = and 330 1.280.258 vf kHz= = = (b) Maximum (i.e. constructive interference) in sound intensity at P if speakers are connected in antiphase. F This question is similar to Lecture Example 10.4.1. If the sources are in phase, first minima occurs when path difference is equa l to half of a wavelength.