Physics 1251 The Science and Technology of Musical Sound

1
Physics 1251The Science and Technology of
Musical Sound

• Unit 1
• Session 9
• Transients and Resonances

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Foolscap Quiz
• What are the following quantities for the
  waveform below? Period, Frequency, Amplitude and
  Phase.

P 5.0 ms 0.0050 sec f 1/P 200. Hz A
2.0 mPa Phase 25 (90)
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• 80/20Period is the time from one point on a wave
  to a corresponding point on the next.
• 80/20Frequency (in Hz) 1/Period (in seconds).
• 80/20Amplitude is the maximum excursion from
  equilibrium for a wave.
• 80/20Phase is the shift (measured in fraction of
  a cycle) for a wave relative to a time standard.

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• 1' Lecture
• Sound carries mechanical energy.
• Frequency spectra can change with time producing
  transients as energy is dissipated by radiation
  and frictional forces.
• Resonance is the strongly driven oscillation,
  occurring at natural frequencies of the natural
  modes of oscillation.

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• 80/20WorkForce x distance movedW F?d .

80/20Energy is the work performed or stored.
E W W Joule Nm
80/20Energy is conserved it changes form but is
never really lost .
80/20Heat is a form of energy.
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• The Simple Harmonic Oscillator of Doom

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Why doesnt the bowling ball return to the same
  height?

1. Energy is conversed, i.e. total energy is
   constant.
2. The bowling ball does work (a little) moving the
   air out of the way. Recall W F?d
3. Therefore, the bowling ball has less energy to
   make it up the hill.

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• 80/20Sound waves carry energy.

80/20Power is the rate of energy dissipation or
radiation. P W/t P Watt Joule/sec
80/20Intensity is the power/square meter. I
P/A I Watt/m 2 .
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Energy Dissipation
• If a constant fraction of the energy is
  dissipated every second, the amplitude of an
  oscillator decays exponentially.

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Damped
• Simple Harmonic Oscillator

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Transients are due to work done by the SHO.

Energy of SHO
Heat
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Where does the lost energy go?

1. Energy is conversed, i.e. total energy is
   constant.
2. The SHO does work (a little each cycle) moving
   the air or water out of the way. Recall W
   F?d
3. Therefore, the SHO slows down a little each
   cycle. It has less energy.
4. Ultimately, the energy goes into heat (random
   motion of air molecules).

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Dr. Ms Energy Conservation Furnace

1. Rub your hands together briskly.
2. What do you feel?
3. Why?

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• 80/20Higher frequencies tend to damp more
  rapidly than do lower frequencies.

Why? ?E Energy dissipated in each cycle
(damping) force x distance. Energy dissipated
per second Energy dissipated per cycle x
cycles per second ?E f.
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Time Dependent Fourier Spectrum
• Observe Transients

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Time Dependent Fourier Spectrum
• Observe Transients

Piano Transient Frequency Spectrum
Amplitude of Component
Frequency
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Resonantly Driven
• Simple Harmonic Oscillator

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Resonantly Driven
• Simple Harmonic Oscillator

Wait 1 period
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Resonance
• An oscillator will absorb energy and grow in
  amplitude when the energy is supplied at a
  frequency near that of a natural mode.

Helmholtz Resonator Video Demonstration
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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Resonantly Driven
• Simple Harmonic Oscillator

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Physics 1251 Unit 1 Session 9 Transients
and Resonances

• Summary
• Transients occur because radiation and friction
  damp the various harmonics differently.
• Resonance is the phenomenon of sympathetic
  vibration at a natural frequency with energy
  supplied by an outside source.
• Sound transmits energy since pressure
  force/area and a displacement occurs as a sound
  wave passes.