Chapter 16 Lecture Three: Wave-I (part 2) HW1 (problems): 16.12, 16.24, 16.27, 16.33, 16.52, 16.59, 17.6, 17.13 Due Friday, Feb. 7.
Superposition of Sinusoidal Waves Assume two waves are traveling in the same direction, with the same frequency, wavelength and amplitude The waves differ only in phase y 1 = A sin ( kx - t ) y 2 = A sin ( kx - t + ) y = y 1 + y 2 = 2 A cos ( /2) sin ( kx - t + /2)
Sinusoidal Waves with Constructive Interference When = 0, then cos ( /2) = 1 The amplitude of the resultant wave is 2 A The crests of one wave coincide with the crests of the other wave The waves are everywhere in phase The waves interfere constructively Af_1803.swf
Sinusoidal Waves with Destructive Interference When = , then cos ( /2) = 0 Also any odd multiple of The amplitude of the resultant wave is 0 Crests of one wave coincide with troughs of the other wave The waves interfere destructively
Sinusoidal Waves, General Interference When is other than 0 or an even multiple of , the amplitude of the resultant is between 0 and 2 A The wave functions still add Use the active figure to vary the phase relationship and observe resultant wave
Sinusoidal Waves, Summary of Interference Constructive interference occurs when = n where n is an even integer (including 0) Amplitude of the resultant is 2A Destructive interference occurs when = n where n is an odd integer Amplitude is 0 General interference occurs when 0 < < n Amplitude is 0 < A resultant < 2A
16.12: Standing Waves If two sinusoidal waves of the same amplitude and wavelength travel in opposite directions along a stretched string, their interference with each other produces a standing wave.
Standing Wave Example
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