for pipes in musical instruments length matters pipes with different lengths in fact produce sounds with different wavelengths therefore frequencies therefore pitches in various instruments the length of the pipe is either fixed such as in a pipe organ or a pan flute or a marimba or it's varied by the player as they play by opening or closing finger Hol or toone holes or keys or valves for example in a pen flute which you're looking at here the length of each pipe is fixed cannot be varied and the player changes frequencies by switching from one cane to another in a church organ is exactly the same thing except that there's a compress the pipes are way too large to be uh blown by mouth and so there has to be an air compressor and air is actually sent by the player plays on a keyboard and that sends through a mechanism compress the air through one or another pipe or very many at the same time that's a pipe organ in the cathedral another Dame in Paris France here the length is not fixed it's a very simple Bamboo Flute which you can make yourself I was actually making them they wer very good they never sounded very well but I was making them when I was a kid just with a bamboo cane and drilling holes into uh the uh the cane itself and uh making sure that I closed alternatively some part some some holes so that when they're all closed the effective length is the entire length of the pipe and when there uh one is open for example the last one it's one bit shorter and the last two it's even shorter and so on and so forth and so the frequency goes up and up and up as the length gets uh shorter shorter shorter um here we have slightly more complicated instruments in which greater length is achieved by having um some some whirling some actual coils in the pipe because that way the instrument is still manageable is still human size and it can be handled easily whereas the length is much longer there are more complex complex instruments such as the saxophone the OBO the clarinet and the bassoon these are uh usually called the brass instruments or the woodwind instrument and uh they actually have a whole set of different mechanisms to change that length of the pipe so one key mechanism is this um piston valves that actually change the path that the air can flow through by opening and closing valves by pressing or not these uh brass Pistons here we have a flugal horn where three pistons and a trigger make the length much longer or much shorter and does uh enable quite a few combinations of different lengths so that multiple notes can be played this is Louie Armstrong one of the greatest trumpet players of all times pipes can be open or closed what I mean by an open pipe is one that's open at both ends so if we look at it in cross-sections um both pipes one looks open open left and right and the other one looks open closed uh left and right respectively a closed pipe on both ends doesn't produce any hearable sound therefore H it's not worth discussing the first mode um actually produces a pressure belly at the center of the acoustic length what do I mean by acoustic length it's actually the length of the pipe plus 0.6 by R where R is the radius of the pipe per opening so here there are two openings in an open pipe and so I will have uh the length of the pipe plus 1.2 uh times the radius um is the effective length is the acoustic length that produces sound that length determines the uh wavelength or rather the half wavelength of the sound produced uh so if we look at the air pressure variation as air travels through we see that there is a belly at the center and uh nodes at both open ends this is the one key thing to always remember at the open end of a pipe there is a pressure node the second mode shows you that there are two Bell bellies so this is one whole wavelength of the sound produced is going to be uh in the acoustic length so now we have two bellies for a closed pipe instead we see that the first mode shows an air pressure node at the open end of the pipe as usual every open end of pipe has a pressure node but it has a pressure belly and the closed end of the pipe so this is one quarter of a sinusoidal wave is one quarter of the sound wavelength so for the second mode instead we have one and a half bellies and so we can see that uh if we summarize all of the modes we have for the open pipe and the close pipe two nodes at the both the open ends of the open pipe and then zero nodes in between uh for the first mode one node two nodes three nodes four nodes for the subsequent modes and so we can see that uh if we count the number of bellies they exactly correspond to the number of the mode and so we have one belly for the first mode two bellies three four five for the second third fourth fifth uh so for the end mode we see that the frequency is always the multiple the end multiple of the fundamental and the fundamental is the speed of sound V sound over twice the acoustic length of the pipe which is the wavelength so as usual frequency equals speed divided by wavelength the four uh this is the usual formula formula exactly how it went for the um string the oscillating string and the modes of a string so we see that here the modes are all there all modes e even and odd modes so n can be equal to 1 2 3 4 five all numbers for a closed piping stead we're going to have a node at the open end of the pipe a belly at the closed end of the pipe so we are going to have only one quarter of a wavelength along the acoustic length of the pipe and so the formula is still the same is still the the velocity divided by the wavelength but now the wavelength is four times the acoustic length to the pipe therefore uh we are going to have half a belly here in the length of the pipe or acoustic length rather uh and the first mode then we're not going to have a a second mode or any other even mode we only have odd modes so here we're going to have three times that half belly so we're going to have one and a half belly and here here we're going to have two and A2 and then three and A2 and four and A2 this are all of the odd modes so if the fundamental is the speed of sound divided by 4 L the uh n mode is going to be once or three times five times seven times nine times the fundamental which correspond to the first mode the third mode the fifth the 7th the 9th the 11th and so on and so forth only the odd modes are present for closed pipes