The Physics of Music PHYS 140 Instructor: Deva O’Neil

The Physics of Music

PHYS 140

Instructor: Deva O’Neil

The Physics of Music(wave mechanics, resonance and acoustics)

vs.

The Music of Physics(sonification: representing physics with music)

What is The Physics of Music?What is The Physics of Music?Week 1: What is a wave? Week 1: What is a wave? Sound waves vs. other wavesSound waves vs. other waves Properties of Sound Properties of Sound Interference of WavesInterference of Waves ChordsChordsWeek 2: Music and AcousticsWeek 2: Music and Acoustics Standing wavesStanding waves Harmonics/overtones/timbreHarmonics/overtones/timbre Resonance / vibrationsResonance / vibrations Standing waves in wind instruments, string Standing waves in wind instruments, string

instruments, percussive instruments, etc.instruments, percussive instruments, etc.Week 3: Miscellaneous topics for Music and Musical Instruments Week 3: Miscellaneous topics for Music and Musical Instruments Musical scales and temperamentsMusical scales and temperaments presentationspresentations

What is a Wave?What is a Wave?

A A wavewave moves energy through space without transporting moves energy through space without transporting the matter itself through spacethe matter itself through space

On Earth, waves often travel through a On Earth, waves often travel through a mediummedium—the —the substance that is being displaced by the wave. substance that is being displaced by the wave.

Examples…Examples… Doing “The Wave” at a sporting eventDoing “The Wave” at a sporting event

Because the matter itself is not traveling, a wave can travel Because the matter itself is not traveling, a wave can travel extremely fast—even faster than light in certain substancesextremely fast—even faster than light in certain substances

Does light need to travel through a medium?Does light need to travel through a medium?

Modes of travelModes of travel

Wave PulseWave Pulse Traveling WaveTraveling Wave Standing WaveStanding Wave

Modes of travelModes of travel

Wave PulseWave Pulse Traveling WaveTraveling Wave Standing WaveStanding Wave

Modes of travelModes of travel

Wave PulseWave Pulse Traveling WaveTraveling Wave Standing WaveStanding Wave

The blue wave is a “standing” wave. It is The blue wave is a “standing” wave. It is the result of combining two traveling the result of combining two traveling waves.waves.

Properties of WavesProperties of Waves

WavelengthWavelength FrequencyFrequency Wave SpeedWave Speed

Wavelength (Wavelength ())

Distance between crests.Distance between crests.

Measured in meters.Measured in meters.

Properties of WavesProperties of Waves

WavelengthWavelength FrequencyFrequency Wave SpeedWave Speed

Frequency (f)Frequency (f)Cycles per second / 0scillations per Cycles per second / 0scillations per

second.second.Measured in Hertz (1 Hz = 1 sMeasured in Hertz (1 Hz = 1 s-1-1).).

Properties of WavesProperties of Waves WavelengthWavelength FrequencyFrequency Wave SpeedWave Speed

Wave Speed (v)Wave Speed (v)Distance covered per unit time.Distance covered per unit time.

Depends on the medium.Depends on the medium.NOT the speed of the molecules in the medium!NOT the speed of the molecules in the medium!

Other PropertiesOther Properties

For a standing wave, it may not be obvious that For a standing wave, it may not be obvious that the wave has a speed, but remember that a the wave has a speed, but remember that a standing wave can be thought of as two traveling standing wave can be thought of as two traveling waves.waves.

Frequency is related to wavelength: f = v/Frequency is related to wavelength: f = v/.. Putting more energy into a wave increases the Putting more energy into a wave increases the

amplitude, but not the speed.amplitude, but not the speed. The The periodperiod of a wave is the number of seconds of a wave is the number of seconds

per cycle. T = 1/f.per cycle. T = 1/f.

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.

A person is standing in the ocean. The height (y) of the water as a function of time is shown in the graph. What’s the period of the wave?

A. ½ secondB. 1 secondC. 1.5 secondsD. 2 seconds

Application: LightApplication: Light

You can tell the frequency of a light wave by the You can tell the frequency of a light wave by the color of the light. color of the light.

The wave speed of light depends only on what The wave speed of light depends only on what medium its traveling through. (As is true of all medium its traveling through. (As is true of all waves.)waves.)

Application: LightApplication: Light

Light is a wave – but what’s “waving?”Light is a wave – but what’s “waving?”

Summary: Properties of Waves

Insert graphs: y(t) and y(x)Insert graphs: y(t) and y(x)

Frequency (f): Number of cycles per secondFrequency (f): Number of cycles per second

Period (T): Number of seconds per cyclePeriod (T): Number of seconds per cycle

Wavelength (Wavelength () : Distance between crests of wave) : Distance between crests of wave

Frequency is related to wavelength: f = v/Frequency is related to wavelength: f = v/

What’s wrong with this What’s wrong with this picture?picture?

Compare 3 waves Compare 3 waves (on the same (on the same string)string)

These are graphs of heights vs. distance (x)These are graphs of heights vs. distance (x)Which has the biggest wavelength?Which has the biggest wavelength?The biggest speed?The biggest speed?The biggest frequency?The biggest frequency?

(A)(A) (B) (B) (C) (C)

2 4 6 8

1 .0

0 .5

0 .5

1 .0

2 4 6 8

1 .0

0 .5

0 .5

1 .0

2 4 6 8

1 .0

0 .5

0 .5

1 .0

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 = 3*108 m/s.

1.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

Digression:The Music of Physics

• What does physics sound like?

• How can you use sound to represent scientific data?

The Music of PhysicsThe Music of PhysicsExamples

“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

Quantum Whistle.mp3

Representing Data with Representing Data with SoundSound

Although this isn’t what this course is about, Although this isn’t what this course is about, it is possible to use music or other non-it is possible to use music or other non-speech audio to represent physical data speech audio to represent physical data (sonification)(sonification)

Two Main Uses:Two Main Uses: Monitors (heart rate monitors, Geiger Monitors (heart rate monitors, Geiger

Counter)Counter) Data RepresentationData Representation

Unexpected Use: Unexpected Use: Catching errors or anomalies in dataCatching errors or anomalies in data

Package

Representing Data with Representing Data with SoundSound

Why?Why?

Potentially useful in teaching (different Potentially useful in teaching (different learning styles)learning styles)

Allows blind people to perceive dataAllows blind people to perceive data Popularization of otherwise obscure Popularization of otherwise obscure

scientific data (see LHC Sound)scientific data (see LHC Sound) More dimensions/variables available than More dimensions/variables available than

visual representationvisual representationHiggsJetSimple.mp3

Visual RepresentationVisual RepresentationPerceptual resources Perceptual resources

available:available:

3 dimensions (one 3 dimensions (one for each axis)for each axis)

ColorColor Time (if can Time (if can

animate)animate)

= 5 dimensions at = 5 dimensions at most (in practice, most (in practice, generally have no generally have no more than 3)more than 3)

Visual RepresentationVisual RepresentationAnother limitation of visual Another limitation of visual

representation:representation: OpacityOpacity

Real life example: Errors in cosmology simulation caught using Real life example: Errors in cosmology simulation caught using audio audio

(not apparent with visual representation due to opacity)(not apparent with visual representation due to opacity)

Movie6.mov

Sonification ToolsSonification ToolsPerceptual resources Perceptual resources

available:available:

PitchPitch Tempo (spacing)Tempo (spacing) LoudnessLoudness DurationDuration Timbre (“color”)Timbre (“color”) Spatialization Spatialization

(stereo)(stereo)

frequencyfrequency

Intensity level Intensity level (aka decibel (aka decibel level)level)

Superposition of Superposition of different wavesdifferent waves

Corresponding Property Corresponding Property of Sound Waveof Sound Wave

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)

Types of Waves

• What type of wave is a radio wave?

• The amount of energy put into a wave determines the…

(a) Speed(b) Frequency(c) Amplitude(d) All of the above

What kind of wave can travel without a medium?