Question

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...

Answer 1

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

Answer 2

...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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

Thank you :)