btec applied science unit 1 physics and this video is about longitudinal standing waves stationary waves i've already done a video about transverse stationary waves which is what you get unlike a guitar string this is about longitudinal stationary waves which is what you get in pipes and tubes now this isn't a stationary wave this is a progressive wave and it is of course its sound and looking at this you can see that there are compressions where the air molecules are close together and these compressions are traveling from left to right this is a progressive wave if you look at any individual particle you'll see it doesn't actually go anywhere it's just oscillating and it's oscillating parallel to the direction that the wave is moving in which is what happens in a longitudinal wave but this is a progressive longitudinal wave this is just another longitudinal wave progressive wave and i've included this because i thought it looked quite nice and it's the one i'm a speaker and again you can see the compressions moving carrying energy but the air particles don't actually go anywhere so this is a progressive longitudinal wave now in musical instruments we get something else we get a stationary wave or a standing wave and what happens is that something produces a vibration it might be a a reed or some kind of a disturbance in the air and then the waves travel up and down the tube and they interfere with each other and they get constructive interference occurring and we get a longitudinal stationary wave very similar to what we get in guitar okay now there are two types of tube that we need to know the first one we're going to look at is where it is closed at one end so we have a tube which is closed at one end and open at the other end so now what you must remember is that a closed end must be a node and an open end must be an antinode a node is where the particles vibrate very very little an antinode is where they vibrate a lot so an open end is an antinode and that means that the the biggest wavelength that we can get is when the length of the tube is equal to a quarter of a wavelength or the wavelength is four times the length of the tube okay so this is our lowest frequency so this is our first harmonic our fundamental and the fundamental occurs when the length of the tube is a quarter of a wavelength what about harmonics now looking at this diagram there's our first harmonic our fundamental we have a node at the closed end an anti-node at the open end now we can't get the second harmonic it would be impossible why can't we get the second harmonic because that would mean there would be a node at the open end and that's not allowed an open end has to be an antinode so we don't get the second harmonic we get the third harmonic which is three times the fundamental frequency we don't get the fourth harmonic we do get the fifth harmonic so if the tube is closed at one end we just get odd harmonics first third fifth etc okay the even harmonics aren't possible this tube is open at both ends and if we follow the rules from before that means that both ends have to be an antinode and we have a node in the middle so the the fundamental frequency is going to be very different and also that the wavelength of the fundamental is going to be very different as well so an air column open at both ends we have an antinode at each end and we have a node in the middle and the length of the air column is half a wavelength this time not quarter of a wavelength half a wavelength again we're going to get different harmonics this time if you look at the first harmonic this time we can get the second harmonic because it would be antinode at both open ends and that's allowed and we get the third harmonic so this time we get all of the harmonics first second third fourth fifth etc now all harmonics are possible so as well as the fundamental frequency being very different the sound the tone of the instrument is very different because we get different harmonics sounds all very complicated let's look at an example an organ pipe has a length of 50 centimeters and it is open at both ends what will be its fundamental wavelength and frequency what other harmonics will be will be present and how would your answers be different if it were closed at one end so i will show you the answers to this one if we look at these tables so the first table open at both ends the length of the air column the length of the organ pipe is 0.5 meters so that means for my first harmonic we remember if it's open at both ends then the length of the tube is half a wavelength so my wavelength is one meter so my fundamental frequency will be 300 hertz if it's open at both ends then we can get all of the harmonics so we'll get my fundamental 300 hertz my second harmonic 600 hertz my third harmonic 900 hertz etc all of the harmonics all the multiples of the fundamental will be present if we close one end of the tube then it'll be very different now my first harmonic is a quarter of a wavelength so my wavelength will be two meters because the wavelength will be four times the length of the tube so my fundamental frequency this time will be 150 hertz if my tube is open at both ends it's 300 hertz if it's closed at one end it's 150 hertz so it'll have a very different fundamental frequency also the second harmonic isn't possible the third harmonic is the fourth harmonic isn't possible the fifth harmonic is we only get the odd harmonics so you'll notice that that the frequencies present will be very different the tube will sound very different okay notice when the pipe is open at both ends the wavelength is half of that of a closed pipe the fundamental frequency is double and we get odd and even harmonics there are different ways you can change the note produced by the instrument there's other factors as well firstly the length of the air column is very important the longer the air column then the bigger the wavelength of the sound so the lower the frequency just imagine a trombone when you make the pipe longer yes the wavelength gets bigger the frequency gets lower uh opening and closing holes along the the length of the air column and a lot of instruments have valves which do this and basically what happens is you are effectively changing the length of the tube and also you're changing what harmonics will be possible an open hole for example on a whistle like this acts as a node and that will affect the effective length of the tube and what harmonics also if you're a very very good trumpet player you can do clever things with your lips which will affect the notes that you get and what harmonics you get as well another factor is the type of mouthpiece okay this will affect the fundamental frequency and also what harmonics you get there are some types of mouthpiece which act like an open end a flute and oboe mouthpiece apparently behave like an open end whereas a clarinet and a trumpet mouthpiece they behave like a closed end and because you only get the odd harmonics they have a brighter harsher sound okay imagine the sound made by a trumpet compared to the sound made by a flute which is a lot sweeter here's a couple of questions you can have a go at a student makes a note by blowing across the end of a wooden pipe 30 centimeters long which is open at both ends okay so have a read of that have a go at it uh very similar to the one that i did earlier on in the video the second one is an example of a six mark question that you might get many musical instruments involve air vibrating inside a tube what factors will affect the frequency and the tone of the notes produced by these instruments and again i've talked quite a bit about this so get some of it learned and be ready for questions like this you