00:01
Okay, in this problem, we want to know why does a pipe that is open at both ends have a different harmonic series than a pipe that is open at one end and close at the other end? well, to understand this, we should look at a picture here, and we can actually draw the same picture as you would for a standing wave on a string, and think of these two nodes here for the strings case as being two pressure nodes in the open.
00:30
In the open pipe case, we have the pipe open at both ends.
00:36
These you can consider as pressure nodes in the open pipe.
00:40
And so here, we know the length of the string, because from node to node, from pressure node to pressure node here, it is going to be a half of a wavelength.
00:51
Solving this for the wavelength gives us 2l.
00:55
And recall that the speed of a wave is always given by the frequency times the wavelength and solving this for the frequency gives us the following equation and we can just substitute our wavelength right here right in and this gives us the fundamental frequency here of this open pipe case and it's going to be the speed of the wave over 2l but now in the case where you have one end closed and and open, now you have only one pressure node and the other side has to be a pressure anti -node.
01:41
And so this from node to antonode is actually a fourth of a wavelength...