Physics of Musical Instruments. Strings viola da gamba cello guitar harpsichord piano electric guitar.

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Presentation transcript:

Physics of Musical Instruments

Strings viola da gamba cello guitar harpsichord piano electric guitar

Strings vibrate with a frequency depending on its length, weight and tension length tension mass per unit length

The length of the part of the string actually vibrating can be changed quickly by the fingers fretless fret

The main problem with all string instruments is: How to make a skinny string move a large amount of air (impedance matching) ? Solution: The string moves a board, the board moves the air

not useful in a hot day very useful in a hot day

Acoustic guitar String vibration body vibration Resonances of the body (and air inside) help transfer the energy from the strings to sound at some frequencies, like the formants in the voice

Some resonances free guitar

Some resonances

Chladni patterns of some resonances

Luthiers try to control the frequencies of these resonances using braces

Plucking the strings at different points changes the timbre See it yourself at

Violin main difference: bowed, not plucked

resonances

Helmholtz (air) resonance

Loudness when playing different notes

Aging of violins: fact or fiction setwins.html

Piano harpsichord

“gravicembalo col piano e forte” (Bartolomeu Cristoforo, 1709) The piano has a hammer instead and it’s possible to control intensity

The sound of the piano is loud AND sustained one single string, overtones filtered out change in decay rate

vertical mode excited initially by the hammer sounding board “gives” faster dumping horizontal mode not initially present sounding board is rigid slower dumping One reason for the two decay rates

Big range in pitch is accomplished by using string of varying thickness thickness length length tension tension Thick string lead to inharmonicities: f, 2f, 3f, 4f, 5f, …, 16f, … f, 2f, 3f, 4f, 5f, …, 16f, … shifted more and more ½ tone higher

F F stretching stretching and deforming

Consequences for tuning f 2.001f... 2f 4f... beating

Consequences for tuning f 2.001f f 4.002f... “stretched octave” tuning

Soundboard

Soundboard

Modes of the soundborad:

Wind instruments oboe flute saxes tuba organ

How to generate oscillation (sound) from continuous blowing ? fipple fipple reed reed

fipple

Simplified, theoretical flute L/2L/2 open end holes closed holes open

Simplified, theoretical flute

embouchure machinery to open/close tone holes metal Modern Boehm flute

semitone mistuning

Reeds

The reed is like the vocal chords and the strings, NOT ! The resonances of the reed are irrelevant, it vibrates with the frequency of the resonances of the column of air

material is irrelevant Boehm fingering

flute, recorder clarinet saxophone, oboe

basssaxophone