SM_PDF_chapter14

# SM_PDF_chapter14 - Superposition and Standing Waves CHAPTER...

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381 Superposition and Standing Waves CHAPTER OUTLINE 14.1 The Principle of Superposition 14.2 Interference of Waves 14.3 Standing Waves 14.4 Standing Waves in Strings 14.5 Standing Waves in Air Columns 14.6 Beats: Interference in Time 14.7 Nonsinusoidal Wave Patterns 14.8 Context Connection Building on Antinodes ANSWERS TO QUESTIONS Q14.1 No. Waves with other waveforms are also trains of disturbance that add together when waves from different sources move through the same medium at the same time. Q14.2 No. A wave is not a solid object, but a chain of disturbance. As described by the principle of superposition, the waves move through each other. Q14.3 They can, wherever the two waves are nearly enough in phase that their displacements will add to create a total displacement greater than the amplitude of either of the two original waves. When two one-dimensional sinusoidal waves of the same amplitude interfere, this condition is satisfied whenever the absolute value of the phase difference between the two waves is less than 120°. Q14.4 When the two tubes together are not an efficient transmitter of sound from source to receiver, they are an efficient reflector. The incoming sound is reflected back to the source. The waves reflected by the two tubes separately at the junction interfere constructively. Q14.5 No. The total energy of the pair of waves remains the same. Energy missing from zones of destructive interference appears in zones of constructive interference. Q14.6 Damping, and non–linear effects in the vibration turn the energy of vibration into internal energy. Q14.7 The air in the shower stall can vibrate in standing wave patterns to intensify those frequencies in your voice which correspond to its free vibrations. The hard walls of the bathroom reflect sound very well to make your voice more intense at all frequencies, and giving the room a longer reverberation time. The reverberant sound may help you to stay on key. Q14.8 The trombone slide and trumpet valves change the length of the air column inside the instrument, to change its resonant frequencies. Q14.9 In a classical guitar, vibrations of the strings are transferred to the wooden body through the bridge. Because of its large area, the guitar body is a much more efficient radiator of sound than an individual guitar string. Thus, energy associated with the vibration is transferred to the air relatively rapidly by the guitar body, resulting in a more intense sound.

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382 Superposition and Standing Waves Q14.10 The vibration of the air must have zero amplitude at the closed end. For air in a pipe closed at one end, the diagrams show how resonance vibrations have NA distances that are odd integer submultiples of the NA distance in the fundamental vibration. If the pipe is open, resonance vibrations have NA distances that are all integer submultiples of the NA distance in the fundamental.
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• Fall '07
• MahaAshour-Abdalla
• Standing wave, Hz

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