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The Principle of Linear Superposition and Interference Phenomena

The Principle of Linear Superposition and Interference Phenomena. 17.1 The Principle of Linear Superposition and 17.2 Constructive and Destructive Interference of Sound Waves. 17.1 The Principle of Linear Superposition. Often two or more wave pulses move through the same space at once

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The Principle of Linear Superposition and Interference Phenomena

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  1. The Principle of Linear Superposition and Interference Phenomena 17.1 The Principle of Linear Superposition and 17.2 Constructive and Destructive Interference of Sound Waves

  2. 17.1 The Principle of Linear Superposition • Often two or more wave pulses move through the same space at once • When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from individual waves

  3. Two Examples

  4. Example • After 2 seconds, what is the height of the resultant pulse at x = 2, 4, and 6 cm? • 0, -2, 2

  5. 17.2 Constructive and Destructive Interference of Sound Waves • Imagine that there are 2 speakers facing each other. Both speakers produce the same sound at the same time.  = 1 m

  6. Destructive interference • One of the speakers is moved back half a wavelength

  7. Noise-canceling ear phones

  8. Problem Solving Strategy • For two wave sources vibrating in phase, a difference in path lengths that is zero or an integer number of wavelengths leads to constructive interference • A difference in path lengths that is a half-integer number of wavelengths leads to destructive interference.

  9. Overlap of Sound

  10. Example – What does the listener hear? • A listener hears two speakers. The distance between the speakers and the listener are 3.00 m and 5.25 m. The sound is at 229 Hz and the speed of sound is 343 m/s. Does the listener hear a loud or soft sound? • Soft sound

  11. Practice Problems • Try sounding out these exercises • 506 CQ 1, P 1 – 3, 6 – 7 • Total of 6 Problems

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