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Photograph of two people playing a marimba with gourds as resonance chambers.
Resonance has been used in musical instruments since prehistoric times. This marimba uses gourds as resonance chambers to amplify its sound. (credit: APC Events, Flickr)

We have emphasized sound applications in our discussions of resonance and standing waves, but these ideas apply to any system that has wave characteristics. Vibrating strings, for example, are actually resonating and have fundamentals and overtones similar to those for air columns. More subtle are the resonances in atoms due to the wave character of their electrons. Their orbitals can be viewed as standing waves, which have a fundamental (ground state) and overtones (excited states). It is fascinating that wave characteristics apply to such a wide range of physical systems.

Describe how noise-canceling headphones differ from standard headphones used to block outside sounds.

Regular headphones only block sound waves with a physical barrier. Noise-canceling headphones use destructive interference to reduce the loudness of outside sounds.

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How is it possible to use a standing wave's node and antinode to determine the length of a closed-end tube?

When the tube resonates at its natural frequency, the wave's node is located at the closed end of the tube, and the antinode is located at the open end. The length of the tube is equal to one-fourth of the wavelength of this wave. Thus, if we know the wavelength of the wave, we can determine the length of the tube.

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Phet explorations: sound

This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.

Sound

Section summary

  • Sound interference and resonance have the same properties as defined for all waves.
  • In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
  • The resonant frequencies of a tube closed at one end are:
    f n = n v w 4 L n = 1, 3, 5 . . ., size 12{n=1,3,5 "." "." "." } {}
    f 1 size 12{f rSub { size 8{1} } } {} is the fundamental and L size 12{L} {} is the length of the tube.
  • The resonant frequencies of a tube open at both ends are:
    f n = n v w 2 L n = 1, 2, 3 . . . size 12{n=1,3,5 "." "." "." } {}

Conceptual questions

How does an unamplified guitar produce sounds so much more intense than those of a plucked string held taut by a simple stick?

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You are given two wind instruments of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency?

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What is the difference between an overtone and a harmonic? Are all harmonics overtones? Are all overtones harmonics?

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Problems&Exercises

A “showy” custom-built car has two brass horns that are supposed to produce the same frequency but actually emit 263.8 and 264.5 Hz. What beat frequency is produced?

0.7 Hz

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What beat frequencies will be present: (a) If the musical notes A and C are played together (frequencies of 220 and 264 Hz)? (b) If D and F are played together (frequencies of 297 and 352 Hz)? (c) If all four are played together?

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What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?

0.3 Hz, 0.2 Hz, 0.5 Hz

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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