What is a wave?

•A disturbance which propagates through a medium. •A means by which energy can be transported.

Wave Medium

Pulse Rope

Sound Air

Water Water

1-dimensional waves: phet string wave

2-dimensional waves:

Falstad ripple

2 kinds of waves:

Transverse – Motion is at right angles to

direction of travel Longitudinal -- Motion is in direction (and anti-

direction) of wave travel (Sound is this kind of wave)

Types of waves

A java animation comparing wave types

Wave simulations in Java

A traveling transverse wave simulation

A traveling longitudinal wave simulation

Waves normally have a “medium” the substance which is disturbed

The medium for sound is normally air phet kinetic theory

How a sound wave travels through air:

phet wave interference (choose sound tab at

top)

The speed of sound – how fast the pattern travels

Roughly 344 m/s through air.

Sound causes a rapid change in air pressure at a point in space – what is

pressure?

Pressure = force / area

• Unit is Newtons/meter2 = Pascal

• 1 N/m2 = Pa

• Can also be measured in atmospheres (1 atm = 101.3 kPa)

Waves and Vibrations

Frequency – How often something happens

We have this class 3 times per week The sun rises 365 times per year The wave emitted by that oboe causes the pressure

at this location of space to reach a crest 500 times per second

500 times per second = 500 hertz = 500 Hz

Scales and intervals • http://www.pianoworld.com/fun/javapiano/javapiano.htm

http://www.frontiernet.net/~imaging/play_a_piano.html • http://www.lon-capa.org/~mmp/applist/sound/sound.html

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/music/piano/sax.htm

http://en.wikipedia.org/wiki/Musical_intervals#Main_intervals

Wave form – the shape of the pattern which is travelling

• phet fourier

Simple Harmonic Motion

-- Linear restoring force.

Simple Harmonic Motion

Unstretched position Spring

pushes down Spring

pulls up

Equilibrium position: no net force

Sinusoidal motion If a system meets the requirements for SHM, the resulting motion will follow a curve called a sinusoid (or a sine curve).

Important features in SHM

Note that the frequency and period are inversely related where: f = 1/T

Frequency and Period

Period = time for one cycle

•measured in seconds (or some other time unit)

Alternatively:

Frequency = number of cycles completed in 1 second

•so measured in cycles per second or hertz.

•1 hertz = 1 Hz = 1 cycle/second

The mass-spring system

Period depends on mass and spring strength, but not on amplitude.

Mass moves fastest as it passes through equilibrium position

Damped harmonic motion

The amplitude, but NOT the frequency decreases with time.

Driven Oscillations and Natural Frequencies

• All mechanical systems have a natural or resonant frequency. – a mass on the end of a spring – a rattling car window – a pendulum

• An external force with the same f as the natural f of the object will “drive” the object causing its amplitude to increase dramatically.

A fundamental equation for ALL

WAVES v= fλ

v = wave speed, [v] = m/s f = frequency, [f] = 1/s = Hz (Hertz) λ = wavelength, [λ] = m

Very Important!

The speed of a wave is ENTIRELY determined by the CHARACTERISTICS of the medium in which it is moving! If the medium is not changed then the wave speed cannot change!

Speed of sound in various materials

Substance Speed (m/s)

Air 344 Helium 965 Water 1482 Lead 1960 Steel 5960 Granite 6000

Source Size:

Whatever the oscillating materials, the bigger it is, the lower the frequency:

v = f λ

For something like a violin, you get to choose the wave speed. For a

wind instrument, you have no choice: you must use the speed of

sound in air.

The Ear

• Anatomy of the ear -- click to page 8

Chapter 6 Human Hearing: Part I

The auditory system Outer ear: channel sound waves to the ear drum. Middle ear: transfers sound wave from ear drum to inner ear. The pressure of the sound wave is amplified substantially. Inner ear: signal processing of the sound wave Frequency range: from about 20 Hz to 20 kHz

The place theory of hearing

The basic pitch determination mechanism is based on the location along the basilar membrane where the hair cells are stimulated. Note the Basilar membrane is about 3.5 cm in length.

Base (near the oval window)

The Basilar membrane is narrow and stiff near the base (oval window end) and wide and floppy at the other end. High frequencies cause the narrow end to vibrate and low frequencies the wide end. When the Basilar membrane vibrates it stimulates the hair cells in that region.

An animated version of the motions of the Basilar membrane

Sources of Sound

Classes of Musical Instruments

String – string is frictionally excited and vibrates Wind -- vibrating column of air Percussion -- usually struck, a 2D or 3D object

vibrates Some instruments are difficult to classify, e.g.

piano

String instruments

String vibrates at a specific pitch

Bowed string instruments:

Plucked string instruments

Struck string instruments

Why is the instrument body needed? Why not just the string?

“you can’t fan a fire with a knitting needle”

Waves reflect off the ends (where the strings are secured)

Ends are nearly rigidly secured. http://phet.colorado.edu/en/simulation/wave-

on-a-string

If the string has no stiffness (only tension), waves are non-dispersive (i.e. different wavelengths travel at

the same speeds)

The difference between travelling waves and standing waves

• http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

• http://phet.colorado.edu/en/simulation/wave-on-a-string

For a string, only certain patterns of waves “fit” as standing waves

http://www.falstad.com/loadedstring/

Wind instruments

Wind column oscillates at a specific pitch

Mechanical wind instrument: Pipe organ

Pipes work like large whistles

A woodwind acts like an organ pipe – but you get to choose the length

on the fly

Woodwinds are among the most ancient musical instruments

30,000-45,000 year old examples have been found.

sound of an ancient flute

The Flute Family

The flutes are (from left to right and, not to be confused with the piano): FLUTE (C FLUTE), PICCOLO, BASS FLUTE, ALTO FLUTE, CONTR'ALTO FLUTE, CONTRABASS FLUTE, 8 feet in length, and the SUB CONTRABASS FLUTE IN G, a full 12 feet in length.

Q) Why is it possible to bend the tubes in such crazy shapes?

Tube open at both ends: Pressure has to be at atmospheric pressure at the

ends

Tone hole size

Effective pipe length = acoustical length. It can be changed by the tone hole size and by the diameter of the tube itself (end correction).

Bassoon tone: Variety makes the instrument:

Historical Brass Instruments

• In today's brasses, finger holes and keys have completely disappeared, having been replaced by valves and slides.

Brasses

The French horn (natural horn) • In the 18th century, prior to the development of the valve, players learned

to change the pitch of the instrument by inserting a hand into the bell, hand stopping.

• To play the instrument in a different key, sections of tubing of different lengths called crooks could be swapped into and out of the instrument.

A horn and its crooks

The source of the sound files

Tube; tube and bell; tube, bell and mouthpiece

Piston valves (trumpet, tuba) and rotary valves (French horn)

hose-a-phone trio

hose-a-phone Rondeau

Percussion instruments

Drums and cymbals in slow motion

• http://www.youtube.com/watch?v=osFBNLA7woY

• http://www.youtube.com/watch?v=1oLtzrAsIgU

http://www.falstad.com/circosc/

For percussion instruments:

Loudness depends on size of surface moving and amplitude

Sound is transient Sound is usually unpitched (may give overall

sensation of high (e.g. triangle) or low (e.g. gong)

(though some instruments (marimba, tympani, etc.) do give a sensation of pitch)

The human voice

Helium and Voice Timbre

• Listen to normal speech. • Speech with helium-filled lungs. • Normal singing. • Singing with helium – what happens

to the pitch?

Resonance curve of vocal tract filled with air

Resonance curve of vocal tract filled with helium

The vertical lines indicate the frequencies of the vocal folds. Q) Why don’t the vocal fold frequencies change in helium? The speed of sound is greater in helium, so the formants occur at higher frequencies: the second formant has been shifted off scale to the right in this diagram. The shift of the formant frequencies causes strong changes in the timbre of the voice.

Reverse effect with Sulfur Hexaflouride: http://www.youtube.com/watch?v=d-XbjFn3aqE

Beats

The Doppler effect