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Chapter 11: Vibrations and Sound

Created by: CK-12

Credit: Martin Thomas
Source: http://www.flickr.com/photos/martin_thomas/7707159728/
License: CC BY-NC 3.0

Waves are periodic motion that induces motion beside it.  One model for this is a crowd wave, where you stand up and sit back down when the person beside you does.  A similar transfer happens when a rope is snapped or sound emitted.  This chapter covers the properties of waves as they move through a physical medium, focusing on sound in particular. 

Chapter Outline

Chapter Summary

  1. Waves may interfere constructively or destructively, giving rise to increases and decreases of the amplitude.
  2. Wave interference is responsible for the phenomenon of beats; where the amplitude of the sound changes when two sounds with close frequencies f_1 and f_2 are produced. The resulting beat frequency is f_b = f_2 - f_1.
  3. The intensity of a wave is defined as the average power produced by some source divided by the surface area over which the energy is transmitted. The equation for the intensity is I = \frac{W}{A} where I represents intensity, W power (the wattage) and Athe area over which the energy, in a given amount of time, has spread.
  4. The range of human hearing is 20 Hz-20,000Hz. Frequencies higher than this are called ultrasonic frequencies.
  5. The wave velocity equation is v = \lambda f where v is the velocity with which the wave travels; \lambda is the wavelength of the wave; and fis the frequency of the wave.
  6. Many objects possess a natural or resonant frequency with which they vibrate. Strings and pipes (tubes) have multiple resonant frequencies as do most musical instruments. During resonance the amplitude of vibration of an object increases dramatically.
  7. Both fixed strings and open pipes have resonant wavelengths of \lambda_n = \frac{2}{n}L, where L is the length of the string that is in resonance, and n = 1,2,3\ldots.
  8. Both strings fixed at only one end and closed pipes have resonant wavelengths of \lambda_n = \frac{4}{n}L where L is the resonant length of pipe or tube, and n = 1,3,5 \ldots.
  9. The Doppler effect occurs when a source of sound and/or the receiver are in motion.

f' = \frac{v '}{\lambda '}  = f \left( \frac{v + v_r}{v + v_s} \right)

A source moving at v_s changes the wavelength.  The source moving away stretches out the wavelength, giving positive v_s.

A receiver moving at v_r changes the effective wave speed.  The receiver moving towards the source makes the waves arrive faster, giving positive v_r.

Image Attributions

  1. [1]^ Credit: Martin Thomas; Source: http://www.flickr.com/photos/martin_thomas/7707159728/; License: CC BY-NC 3.0

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At Grade

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Date Created:

Jun 10, 2014

Last Modified:

Sep 06, 2014
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