Music and Resonance

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Music and Resonance
Introduction to Acoustics

• University of Salford
• Acoustics Audio and Video Group

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Learning Outcomes

• Explain how string and wind musical instruments
  produce sound
• Explain the concepts of resonance, mode and
  harmonic
• Calculate modal frequencies for a stretched
  string and a pipe

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Resonance

• Any finite body
• Natural frequencies
• Response curve (force with swept sine)

or
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Examples
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Basic questions

• How does a guitar work?
• What controls the pitch of the guitar sound?

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Vibrating string

• Wavelength
• Speed
• Frequency

T is tension ? is mass per unit length
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Pitch and frequency

• Pitch is closely related to fundamental
  frequency, f1
• f1 is the frequency of the first mode
• f1 increases as tension T is increased
• f1 decreases as length L is increased

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Higher modes
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Harmonic Series

• When a guitar string is plucked, it vibrates in
  several modes at once
• We sometimes call the modes harmonics
• The frequencies are harmonically related f22
  f1 f33 f1 and so on

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Example
A piano string is made from a 0.75 m long steel
wire with a mass per unit length of 1.4 x 10-2
kgm-1. If the string is subjected to a tension of
100 N, what will its fundamental frequency
be? (Next tutorial sheet 12, question 4)
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Resonance in closed pipes
Also get f2, f3, etc
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Resonance in half-open pipes
Note only odd modes present
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Resonance in bridges
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Conclusions

• All finite bodies have resonances
• An object is easy to excite at its resonant
  frequencies
• Musical instruments have harmonic resonant
  frequencies
• Pitch is tied to fundamental frequency