Calculating Resonant Lengths of Air Columns

[soulja101]

Homework Statement

The 3rd resonant length of a closed air colum is 75cm. determine the 1st and second length.

Homework Equations

the rensonant patterns

The Attempt at a Solution

i just don't get this resonant things.

 

[berkeman]

How many sinusoidal periods are in a resonant length? I'm not familiar with air column resonances, but for stringed instruments like a guitar, the fundamental is when there is a half-sine wave shape on the string as it vibrates. That is, the ends are fixed, and the middle is what moves back and forth to make the sound. So the 2nd harmonic has a full sine wave shape on the string as it vibrates (the middle doesn't move, and each half of the string vibrates back and forth. The 3rd harmonic has 3 half-sines on the string, etc.

Now, you need to first figure out what the fundamental consists of in an air column (it's a pressure wave for air, obviously), and then think in terms of adding in half-periods as you move up through the harmonics...

 

[brewnog]

A closed air column behaves in the same way as a string, in as far as resonant harmonics are concerned...