Harmonics on a String

Phys 1240: Sound and Music LAST: harmonics, perception and ears CT ex-TG

TODAY: spectra Shouldn't concept tests be worth double, the class before NEXT: Enjoy your break! Thanksgiving break? Next Tues - more on spectra, back to instruments. A) Yes indeedy

Reading: 8.3 (AM/FM) B) Of course 10.2 (vibrations in string instruments) C) Why not? 12.1 (vibrations in wind instruments) D) Seems only fair to me. E) No!

Hair cell

ccrma.stanford.edu/courses/220a-fall-2001/dancingHairCell.mpg

Harmonics on a string

From last week’s long answer: fn = n " f1 “Why do the frets of a guitar get closer together as you move up the ﬁngerboard?” You usually hear several of these ! Harmonics simultaneously. Do you think you need to have ever held/played a guitar to Which ones are present answer this question? (and how strong) does NOT (much) impact “pitch” you hear, But => BIG impact on the TIMBRE (“character”) of sound.

1 Example: Continuing this example:

f1 2f 3f f1 1 1 Amplitude A1 (medium!)

(medium) (small) (big) f2 =2f1 Frequency SPECTRUM: Amplitude A2 (Rather small) Ampl.

f3 =3f1

Amplitude A3 3f (Rather big) f1 2f1 1 frequency

Example: Example:

3f1 3f1 2f 2f f1 1 f1 1

(small) (medium) (big) (small) (medium) (big) Frequency SPECTRUM: Frequency SPECTRUM:

Ampl. ? Ampl.

3f 3f f1 2f1 1 f1 2f1 1 frequency frequency

2 Ct8.2.1 Consider a sound which decomposes into the following waves: Spectral analysis 4f1 f1 2f1

Fourier simulation The frequency spectrum looks like: e d u t i l A p B m a phet.colorado.edu/simulation-pages/sound-simulations.htm f 5f f 5f 1 freq 1 1 freq 1 e d u t i l C

p D m a

f 5f1 f1 5f 1 freq freq 1 E) Something else

CT8.2.3 Ct 8.2.3b You’re listening to a computer-tone which contains TWO harmonics: the fundamental (f1 = 100 Hz) A string has fundamental f1. + the 6th harmonic (f6=600 Hz). What is the spacing (the difference) between two What frequency do you (likely) perceive? successive higher harmonics?

A) 100 Hz A) That would be f1 also B) 500 Hz B) It varies, it depends on “n”. C) 600 Hz D) 700 Hz E) Something totally different

3 Spacing between harmonics: CT8.2.4 You’re listening to a computer-tone which contains 200, 300, 400 and 500 Hz, but is missing 100 Hz.

f1 f1 What is the fundamental frequency? (i.e. what is the frequency at which the combined tone repeats itself?) f 2f 3f 4f 5f 6f 1 1 1 1 1 1 A) 100 Hz B) 200 Hz C) Something totally different

What frequency do you (likely) perceive?

Ct8.2.2 Ct8.1.1a An ideal string instrument has a Consider the following waveforms: fundamental frequency of f1. Which of the following frequency spectra is most unlikely? e e d d u u t t i i True (A) or False (B): Both have the l l B p

A p m m same fundamental frequency a a f f 1 6f1 1 6f1 e e d d u t u i t l i l p C D p m m a a

f1 6f 1 f1 6f1 E: (All are fine, or else several are completely unphysical)

4 Ct8.1.1b Consider the following waveforms: Real spectra

Ideal instruments produce only sounds at exact (harmonic) True (A) or False (B): Both have the frequencies same frequency spectra. Real sounds contain all frequencies (but with peaks at the harmonics!)

Anharmonic sounds (e.g. drums) don’t have such simple patterns.

AudioXplorer

CT ex-TG2

Which is better?

A) Turkey B) Tofu