Limit to number of standing waves in pipes?

[eknox123]

Homework Statement

This is a conceptual question I had not related to a specific problem- so I know with each higher harmonic in pipes that the frequency increases a certain amount (the fundamental frequency- and that in pipes closed at one end skips the even harmonics). However I also know that frequency is inversely proportionate to wavelength. So each successive harmonic has a smaller wavelength. But since there's a limit (I assume) to how small a wavelength can be, does each pipe have its own limit in terms of the number of harmonics that can be made in it?

Homework Equations

v= wavelength * frequency

The Attempt at a Solution

As I wrote above, I'm guessing there is a limit- like the highest harmonic is the one with the lowest non-zero wavelength (that will be the highest frequency), but I'm not sure if my class is oversimplifying it, and really there are exceptions or something

 

[tiny-tim]

welcome to pf!

hi eknox123! welcome to pf!

… frequency is inversely proportionate to wavelength. So each successive harmonic has a smaller wavelength. But since there's a limit (I assume) to how small a wavelength can be, does each pipe have its own limit in terms of the number of harmonics that can be made in it?

i suppose that when you get near the molecular level, the random thermal vibrations predominate, and the equations stop working, and so you can't have wavelengths shorter than that …

but I'm guessing that's a lot higher-pitched than any ear can hear! ​