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Traveling Waves: Superposition

Traveling Waves: Superposition. Wave Superposition:. Add the two waves together (superposition of wave 1 and wave 2) as follows:. Traveling Waves: Superposition. Wave Superposition:. Wave 2. Superposition!. Wave 1. The intensity of the new wave is proportional to A 12 squared!.

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Traveling Waves: Superposition

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  1. Traveling Waves: Superposition • Wave Superposition: Add the two waves together (superposition of wave 1 and wave 2) as follows: PHY 2053

  2. Traveling Waves: Superposition • Wave Superposition: Wave 2 Superposition! Wave 1 The intensity of the new wave is proportional to A12 squared! PHY 2053

  3. Traveling Waves: Superposition • Wave Superposition: Consider two waves with the same amplitude, frequency, and wavelength but with an overall phase difference of DF = f. sinA+sinB = 2sin[(A+B)/2]cos[(A-B)/2] Superposition! New intensity! New amplitude! PHY 2053

  4. Traveling Waves: Interference • Maximal Constructive Interference: Consider two waves with the same amplitude, frequency, and wavelength but with an overall phase difference of DF = 2pn, where n = 0, ±1, ±2,… Max Constructive! • Maximal Destructive Interference: Consider two waves with the same amplitude, frequency, and wavelength but with an overall phase difference of DF = p+2pn, where n = 0, ±1, ±2,… Max Destructive! PHY 2053

  5. Example Problem: Superposition • Two traveling pressure waves (wave A and wave B) have the same frequency and wavelength. The waves are superimposed upon each other. The amplitude of the resulting wave (wave C) is 13 kPa. If the amplitude of wave A is 12 kPa and the phase difference between wave B and wave A is fB – fA = 90o, what is the amplitude of wave B and the magnitude of the phase difference between wave A and wave C, respectively? Answer: 5 kPa, 22.62o PHY 2053

  6. Traveling Waves: Superposition • Lateral Phase Shift: Consider two waves with the same amplitude, frequency, and wavelength that are in phase at x = 0. Wave 1 distance d1 Wave 2 distance d2 Max Constructive Max Destructive PHY 2053

  7. Examples: Superposition Dd = l/2 max destructive Dd = l max constructive Dd = l/4 PHY 2053

  8. Example Problem: Superposition x • The figure shows four isotropic point sources of sound that are uniformly spaced on the x-axis. The sources emit sound at the same wavelength l and the same amplitude A, and they emit in phase. A point P is shown on the x-axis. Assume that as the sound waves travel to the point P, the decrease in their amplitude is negligible. What is the amplitude of the net wave at P if d = l/4? Answer: Zero Max Destructive PHY 2053

  9. Example Problem: Superposition • Sound with a 40 cm wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle as shown in the figure. Part of the sound wave travels through the half-circle and then rejoins the rest of the wave, which goes directly through the straight portion. This rejoining results in interference. What is the smallest radius r that results in an intensity minimum at the detector? Point B Point A Answer: 17.5 cm At point A the waves have the same amplitude, wavelength, and frequency and are in phase. Wave 1 travels a distance d1 = 2r to reach the point B, while wave 2 travels a distance d2 = pr to reach the point B. Max Destructive PHY 2053

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