The Physics of Music

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The Physics of Music

• PHYS 140
• Instructor
• Deva ONeil

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• The Physics of Music
• (wave mechanics, resonance and acoustics)
• vs.
• The Music of Physics
• (sonification representing physics with music)

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What is The Physics of Music?

• Week 1 What is a wave?
• Sound waves vs. other waves
• Properties of Sound
• Interference of Waves
• Chords
• Week 2 Music and Acoustics
• Standing waves
• Harmonics/overtones/timbre
• Resonance / vibrations
• Standing waves in wind instruments, string
  instruments, percussive instruments, etc.
• Week 3 Miscellaneous topics for Music and
  Musical Instruments
• Musical scales and temperaments
• presentations

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What is a Wave?

• A wave moves energy through space without
  transporting the matter itself through space
• On Earth, waves often travel through a mediumthe
  substance that is being displaced by the wave.
• Examples
• Doing The Wave at a sporting event
• Because the matter itself is not traveling, a
  wave can travel extremely fasteven faster than
  light in certain substances
• Does light need to travel through a medium?

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Modes of travel

• Wave Pulse
• Traveling Wave
• Standing Wave

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Modes of travel

• Wave Pulse
• Traveling Wave
• Standing Wave

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Modes of travel

• Wave Pulse
• Traveling Wave
• Standing Wave
• The blue wave is a standing wave. It is the
  result of combining two traveling waves.

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Properties of Waves

• Wavelength
• Frequency
• Wave Speed
• Wavelength (l)
• Distance between crests.
• Measured in meters.

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Properties of Waves

• Wavelength
• Frequency
• Wave Speed
• Frequency (f)
• Cycles per second / 0scillations per second.
• Measured in Hertz (1 Hz 1 s-1).

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Properties of Waves

• Wavelength
• Frequency
• Wave Speed
• Wave Speed (v)
• Distance covered per unit time.
• Depends on the medium.
• NOT the speed of the molecules in the medium!

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Other Properties

• For a standing wave, it may not be obvious that
  the wave has a speed, but remember that a
  standing wave can be thought of as two traveling
  waves.
• Frequency is related to wavelength f v/l.
• Putting more energy into a wave increases the
  amplitude, but not the speed.
• The period of a wave is the number of seconds per
  cycle. T 1/f.

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A person is standing in the ocean. The height
(z) of the water as a function of time is shown
in the graph. How many periods are represented
by this interval (between the two dots)?
? ?
A. Half of one period. B. Exactly one
period. C. Two periods. D. One and a half periods.
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A person is standing in the ocean. The height
(y) of the water as a function of time is shown
in the graph. Whats the period of the wave?

A. ½ second B. 1 second C. 1.5 seconds D. 2
seconds
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Application Light

• You can tell the frequency of a light wave by the
  color of the light.
• The wave speed of light depends only on what
  medium its traveling through. (As is true of all
  waves.)

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Application Light

• Light is a wave but whats waving?

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Summary Properties of Waves

Insert graphs y(t) and y(x) Frequency (f)
Number of cycles per second Period (T) Number
of seconds per cycle Wavelength (l) Distance
between crests of wave Frequency is related to
wavelength f v/l
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Whats wrong with this picture?
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Compare 3 waves (on the same string)These are
graphs of heights vs. distance (x)

• Which has the biggest wavelength?
• The biggest speed?
• The biggest frequency?
• (A) (B) (C)

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• A certain radio wave has a wavelength of about
  3.1 meters.
• Radio is a type of light wave, so if it is
  traveling in empty space, its speed is c 3108
  m/s.
• What is the frequency of the wave?
• (FM waves are usually defined in MegaHertz 1
  MHz 1000,000 Hz.)
• 2. What is the period of the wave?
• 3. AM radio waves have a much longer wavelength
  (closer to 300 meters). Do you think they have a
  smaller frequency or larger frequency?

PhET simulation Radio
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DigressionThe Music of Physics

• What does physics sound like?
• How can you use sound to represent scientific
  data?

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The Music of Physics

• Examples
• Quantum Whistle The sound of supercooled
  helium liquid forced through a small opening,
  producing vibrations as vortices force it to slow
  down
• NASA, Voyager I Mission

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Representing Data with Sound

• Although this isnt what this course is about, it
  is possible to use music or other non-speech
  audio to represent physical data (sonification)
• Two Main Uses
• Monitors (heart rate monitors, Geiger Counter)
• Data Representation
• Unexpected Use
• Catching errors or anomalies in data

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Representing Data with Sound

• Why?

• Potentially useful in teaching (different
  learning styles)
• Allows blind people to perceive data
• Popularization of otherwise obscure scientific
  data (see LHC Sound)
• More dimensions/variables available than visual
  representation

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Visual Representation

• Perceptual resources available

• 3 dimensions (one for each axis)
• Color
• Time (if can animate)
• 5 dimensions at most (in practice, generally
  have no more than 3)

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Visual Representation

• Another limitation of visual representation

• Opacity

Real life example Errors in cosmology
simulation caught using audio (not apparent with
visual representation due to opacity)
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Sonification Tools

• Perceptual resources available

Corresponding Property of Sound Wave

• Pitch
• Tempo (spacing)
• Loudness
• Duration
• Timbre (color)
• Spatialization (stereo)

• frequency
• Intensity level (aka decibel level)
• Superposition of different waves

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Review

• Identify each of the following as a frequency, a
  period, or a wavelength
• 12 cm
• 500 Hz
• 3 seconds
• 9 per second (or, 9 s-1)

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Types of Waves

• What type of wave is a radio wave?
• The amount of energy put into a wave determines
  the
• Speed
• Frequency
• Amplitude
• All of the above
• What kind of wave can travel without a medium?