An air column open at both ends has a 3rd resonant length of 45 cm. What is the 4th resonant length?

Question

An air column open at both ends has a 3rd resonant length of 45 cm.  What is the 4th resonant length?

anonymous · Answer

Multiply by three to find the length of the air column; divide by four to get the fourth resonant length.

anonymous · Answer

But why do we multiply it by 3 and divide it 4? Do we do that to all these type of questions? What is the theory behind this? Thanks :)

anonymous · Answer

Well, if its the third harmonic, then there are going to be three pressure maxima, and in the fourth, you have four, so it's just a matter of finding the length of the tube, and then dividing appropriately to find the new length. This may help: http://en.wikipedia.org/wiki/File:Moodswingerscale.svg