0:00
I welcome you to this video in which you will learn how to calculate the frequency of a wave in an open tube and in a closed tube. And for this we are going to solve the following exercise. What is the frequency of the third harmonic of a sound wave that travels in an air-to-air tube? If this tube has a length of 70 centimeters. Incise A if the tube is open. Incise B if the tube is closed.
0:30
We are going to remember that the speed of sound in the air at ambient temperature is 343 m/s. To be able to calculate this frequency of the third harmonic of that sound wave, we are going to use the following formula whenever we are talking about an open tube. Be careful, the formula is different for open tubes than for closed tubes. Trying to solve our incision A, which refers to an open tube, the formula would be the following:
1:00
In this formula it tells us that in order to find the resonance frequency of a certain harmonic of a wave, we would have to multiply the harmonic number we are talking about by the speed of sound
1:13
and that divide it by 2 for the length of the tube. If in your example it tells you that you have to calculate the frequency of the fifth harmonic, n for you will be 5. If in your example it tells you that you have to calculate the frequency of the second harmonic, n will be 2 and so on. Well, in this case then we are going to try to solve this exercise considering that our harmonic is the third and therefore n is 3.
1:40
It says that we are going to multiply that by V, which would be the speed of sound, which would be 343 meters per second. Later, according to the formula, we are going to divide that by 2 multiplied by the length that that tube has. But be careful, that length has to be expressed in meters.
2:02
Como en este caso, esa longitud no la dan en centímetros, tendríamos que convertir esos centímetros a metros. Solamente hay que dividir entre 100. 70 entre 100 nos da como resultado .7 metros.
2:15
Since we have substituted all our data in that formula, first we are going to multiply 3 by 343 meters over seconds. That gave us 1029 meters over seconds. Then we have that this is dividing between 2 multiplied by 0.7 meters. It gives us as a result 1.4 meters.
2:36
Finally, we have to divide numbers by numbers and units by units. 1029 by 1.4 gives us 735 meters over seconds between meters. These meters that we have here are eliminated with those that are below, and I only have seconds, but they are in the denominator. In other words, I would have 1 over seconds.
3:01
It is important to remember that the frequency ideally has to be expressed in hertz and the hertz are equivalent to 1/2 so this that we have here in other words we would have 735 hertz and ready with this we have already calculated the frequency of the third harmonic in the tube considering that that tube is open.
3:25
Now we are going to solve our B-incision, which tells us that if the tube were closed, what would happen? The formula is very similar, the only thing that is going to change is that instead of having a 2 here, a 4 appears here.
3:38
Anyway, I will explain the procedure again. Remember that N is the harmonic that we are analyzing. If it were the fundamental frequency or if it were the natural frequency, our harmonic would be 1. If we are talking about the second harmonic, our N would be 2 and so on. In this case, as we are analyzing the same harmonic for the open tube as the closed one, N would again be 3 because we are talking about the third harmonic.
4:05
We already know that V is the speed of sound at ambient temperature because in this case here it tells us that we are going to divide it by 4 for the length that this tube has. We already know that here it is in centimeters, we have to change it to meters.
4:21
Finally we make those multiplications 3 by 343, that is the same as it is up here so it will give us this result. Now on the denominator side we have 4 multiplied by 0.7 meters, numbers by numbers and then we have to include the units. Finally we divide 1029 by 2.8 gives us 367.5
4:47
As here we have the same units as above, we already know that we are going to have 1 over seconds and that those at the end are going to be hertz, well, we can advance the process a little here and we already know where these hertz come from that we have pointed out here as the final result.
5:03
When you want to calculate the resonance frequency of a wave in an open tube, this would be the formula. When we are talking about a closed tube, it would be this other one. Remember, the only difference is that here we have a 2 and here is a 4. And very important, when we are analyzing a certain harmonic, if we are talking about an open tube, it can generally be any number. However, when we talk about a closed tube, those antinodes or harmonics
5:32
pueden ser solamente números impares. 1, 3, 5, 7, etc., etc. Y ya con esto concluimos con nuestro video, agradeciéndote por habernos visitado. Si te ha gustado este video, pues te pido que nos regales un like. Que tengas un excelente día.
