Harmonics, Notes, Beat frequency

[Bengo]

Homework Statement

When an instrument plays a note, the resulting sound is a combination of all the possible harmonics for that instrument in its momentary configuration. For instance, a musician changes notes on a violin by pressing the strings against the neck of the instrument, thus shortening the string length and changing the possible harmonics. A given shortened string will play at one time all the possible harmonics allowable by its string length. A given note is the same set of harmonics for all instruments.

1. Doesn't a wavelength have an infinite possibility of harmonics?

2. Why is there no beat frequency if each harmonic has a different frequency.

These aren't actual questions from my study books but they are really confusing to me.

Homework Equations

1. f=nv/2L

2. beat frequency= abs (f1=f2)

The Attempt at a Solution

1. My reasoning for thinking that there is an infinite number of possible harmonics is that you can keep increasing n in f=nv/2L.

2. Maybe there is no beat frequency because the frequencies are not close enough together or maybe the fundamental frequency "envelopes" the rest of the harmonic frequencies?

 

[AlephZero]

1. Doesn't a wavelength have an infinite possibility of harmonics?

2. Why is there no beat frequency if each harmonic has a different frequency.

1. My reasoning for thinking that there is an infinite number of possible harmonics is that you can keep increasing n in f=nv/2L.

In theory that is correct, but the amplitude of the harmonics usually decreases as n increases, and also you can only hear a finite number of harmonics because of the limited range of human hearing (about 20 Hz to 20000 Hz).

The number of audible harmonics in the sound of different instruments can vary from only 2 or 3, up to more than 30.

2. Maybe there is no beat frequency because the frequencies are not close enough together or maybe the fundamental frequency "envelopes" the rest of the harmonic frequencies?

From your formula, the beat frequency between two harmonics m and n is the same frequency as another harmonic, abs(m-n). So "beats between harmonics" don't create anything new in the sound.

 

[rude man]

1.
A given note is the same set of harmonics for all instruments.

No. The thing that distinguishes one instrument from another, all playing the same fundamental frequency (e.g. A=440 Hz which is A above middle C) is the variation in amplitude and phase of the various harmonics.