## Cutiepo0 2 years ago What is the shortest air column, closed at one end, that will resonate at a frequency of 440 Hz when the speed of sound is 344 m/s? I tried using the wavelength= v/f formula, but I keep getting the wrong answer...

1. JamesJ

well you can calculate the wavelength. But how does that wavelength relate to the column of air?

2. JamesJ

...and it depends if it is open or closed. Yours is closed. This might help you: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/opecol.html

3. Cutiepo0

I still don't really know what to do :( I don't know how the length of the column relates to anything

4. Cutiepo0

SO because the wavelength is .8, and in a closed cylinder, the length is 1/4 the wavelength, the answer is .2?

5. luthier93

Wavelength is v/4L for closed tube. Solve that for L to find length.

6. JamesJ

The wave doesn't oscillate at the closed end; it can't. That's why there's a node at that end. At the open end, that's the natural place for an anti-node. So if you drew out one entire wave form 0 to max to 0 to min to 0, you can see that that first anti-node is at the max, and that is 1/4 of the total wave length. So, given f and v, you have solved for wavelength, lambda. Now the length of that tube is L = lambda/4.

7. Cutiepo0

Thank you :)