How does flute work?

Question

I started learning flute a few months ago. Here in India you can buy two types of flute hindustani and carnatic. Hindustani flute has a simple acoustics.

Lenth is inversely proportional to frequency.

When it comes to carnatic flute it gets a bit complicated

if the same theory(length-frequency proportionality) is applied here covering the bottom hole for the first two sounds doesn't make any sense because the length of the open pipe is unchanged with or without covering the bottom hole. Also for the note ma the topmost and bottommost holes are left open but the length of the open pipe is unchanged even if you don't cover the other holes right? Can somebody explain this thing using acoustics?

Is there any other factors affecting the frequency here like the radius of the holes or something like that?

Answer 1

I have not studied these flutes but from general physical principles I can see the following.

First, we recall that a sound wave is a pressure wave, and at the same time a wave in the density of the medium. To understand what is going on, it is usually best to discuss it in terms of pressure.

The main effect of opening or closing a hole is to change the degree to which pressure oscillations can occur at the hole. When the hole is closed, the pressure can oscillate there without any trouble. (A high pressure simply pushes against the wall of the flute and the finger of the player.) When the hole is open, the pressure can still oscillate a bit at the location of the hole, but not as much.

With this in mind, you can regard the first open hole as a providing a location where the pressure wave has a node. (In waves a node is a place of no movement.) This is the main picture. In this picture the other holes are irrelevant. However in practice it is not that simple because the first open hole does not force the node to be exactly under the hole: it could be nearby. By closing some further holes you can adjust the location of the node a bit, and this will adjust the wavelength and hence the tuning of the note.