Standing waves - which instruments are closed-closed, open-open, or open-closed?

[ben.tien]

Homework Statement

Okay. So I'm sort of confused about the concept of determining whether an instrument is closed-closed, open-open, or closed-open.ie. a flute, guitar, sax, oboe, clarinet. For example, is a clarinet a closed-open instrument because your mouth covers the entire mouth piece and the flute is open-open because your mouth doesn't? What are ways one can use to determine this? Thanks in advance.

Homework Equations

fn = v(n/2L) n = 1,2,3,...
fn = v(n/4L) n = 1,3,5,...

The Attempt at a Solution

 

[Stonebridge]

I take it you are happy with stringed instruments. They are clearly all "closed" at both ends. This means the standing wave pattern has a node at both ends, and the fundamental frequency has a wavelength twice the length of the string. The string is able to produce all the harmonics in the series f, 2f, 3f, etc.
With wind instruments it gets a little complicated.
A flute is open at both ends and produces a full set of harmonics. There is an antinode at both ends and the fundamental frequency has a wavelength twice the length of the tube.
Reed instruments (clarinet, oboe, bassoon, oboe etc) are closed at one end and open at the other. This means there is a node at the closed end and an antinode at the open end.
In the case of the clarinet, it is a cylindrical bore, and behaves like a standard "closed" pipe. It only produces odd harmonics (f, 3f, 5f etc) and has a fundamental frequency with a wavelength 4 times the length of the tube.
The other instruments have a conical bore. This complicates the maths a bit, but the result is that the sound that comes out contains the full set of harmonics.
There is a good treatment of this on this page and the various links from it. (It also deals with brass and other instruments)
It is very informative.
http://www.phys.unsw.edu.au/jw/woodwind.html

 

[ben.tien]

Thank you very much!