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

What is a Wave? A wave moves energy through space without transporting the matter itself through space A wave moves energy through space without transporting the matter itself through space On Earth, waves often travel through a medium—the substance that is being displaced by the wave. On Earth, waves often travel through a medium—the substance that is being displaced by the wave.Examples… Doing “The Wave” at a sporting event Doing “The Wave” at a sporting event Because the matter itself is not traveling, a wave can travel extremely 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 travel Wave Pulse Wave Pulse Traveling Wave Traveling Wave Standing Wave Standing Wave

Modes of travel Wave Pulse Wave Pulse Traveling Wave Traveling Wave Standing Wave Standing Wave

Modes of travel Wave Pulse Wave Pulse Traveling Wave Traveling Wave Standing Wave Standing Wave The blue wave is a “standing” wave. It is the result of combining two traveling waves.

Properties of Waves Wavelength Wavelength Frequency Frequency Wave Speed Wave Speed Wavelength ( ) Distance between crests. Measured in meters.

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

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

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. 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/. Frequency is related to wavelength: f = v/. Putting more energy into a wave increases the amplitude, but not the speed. 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. The period of a wave is the number of seconds 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 second B. 1 second C. 1.5 seconds D. 2 seconds

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

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

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 ( ) : Distance between crests of wave Frequency is related to wavelength: f = v/ Frequency is related to wavelength: f = v/

What’s wrong with this picture?

Compare 3 waves (on the same string) 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) (B) (C) (A) (B) (C)

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*10 8 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 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

Representing Data with Sound Although this isn’t 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) Monitors (heart rate monitors, Geiger Counter) Data Representation Data Representation Unexpected Use: Catching errors or anomalies in data

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

Visual Representation Perceptual resources available: 3 dimensions (one for each axis) 3 dimensions (one for each axis) Color Color Time (if can animate) Time (if can animate) = 5 dimensions at most (in practice, generally have no more than 3)

Visual Representation Another limitation of visual representation: Opacity Opacity Real life example: Errors in cosmology simulation caught using audio (not apparent with visual representation due to opacity)

Sonification Tools Perceptual resources available: Pitch Pitch Tempo (spacing) Tempo (spacing) Loudness Loudness Duration Duration Timbre (“color”) Timbre (“color”) Spatialization (stereo) Spatialization (stereo) frequency frequency Intensity level (aka decibel level) Intensity level (aka decibel level) Superposition of different waves Superposition of different waves Corresponding Property of 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) (a) Speed (b) (b) Frequency (c) (c) Amplitude (d) (d) All of the above What kind of wave can travel without a medium?