What constitutes a closed end in acoustic resonance in tubes

[MatthijsRog]

Dear all,

For my students, I'm currently trying out some experiments they can do to simulate acoustic processes. One of the topics that we will be discussing is that of standing waves.

Although I have never done it before--I come from a completely different background--I want to create standing sound waves in a PVC tube. I want to do this by placing a speaker, attached to a function generator, at one end of the tube so that the speaker can generate a "perfect" sine at any frequency the students may wish to experiment with.

Unfortunately, most of the online articles on acoustics are very basic and high school exam-oriented, which leaves me with some practical questions.

Say I put my speaker at one end, and leave the other end open. Will I get resonance belonging to typical acoustic open-open end tube resonances? That is, will my speaker function as an open end, or as a closed end? I'm not sure which one because on one hand, sound can reflect from it and on the other hand it's the obvious choice for an antinode.

And second question: would it be possible to put up two interfaces in the tube, so that a standing wave would form in between those two interfaces? I've done such experiments with light a few times (Fabry-Perot interferometers) but I'm not sure whether it would work with sound.

Thanks for the help in advance.

Matthijs

 

[PeterO]

Dear all,

For my students, I'm currently trying out some experiments they can do to simulate acoustic processes. One of the topics that we will be discussing is that of standing waves.

Although I have never done it before--I come from a completely different background--I want to create standing sound waves in a PVC tube. I want to do this by placing a speaker, attached to a function generator, at one end of the tube so that the speaker can generate a "perfect" sine at any frequency the students may wish to experiment with.

Unfortunately, most of the online articles on acoustics are very basic and high school exam-oriented, which leaves me with some practical questions.

Say I put my speaker at one end, and leave the other end open. Will I get resonance belonging to typical acoustic open-open end tube resonances? That is, will my speaker function as an open end, or as a closed end? I'm not sure which one because on one hand, sound can reflect from it and on the other hand it's the obvious choice for an antinode.

And second question: would it be possible to put up two interfaces in the tube, so that a standing wave would form in between those two interfaces? I've done such experiments with light a few times (Fabry-Perot interferometers) but I'm not sure whether it would work with sound.

Thanks for the help in advance.

Matthijs

I believe the speaker acts as a closed end. I have set up a similar thing with a perforated brass tube (plastic/PVC just catches fire)
I first drilled small holes (use a printed circuit board drill) 2 cm apart from one end to the other in a straight line.
I attached a speaker to one end (actually a strtched a section of a rubber party balloon over first - I got sick of the speaker catching fire and burning out)
I then inserted a a large, one-holed rubber stopper in the other end, with a glass tube through it - which was connected to the gas supply. (bunsun burner gas).
Turning on the gas, you light the gas emanating from the holes to produce a linear birthday cake effect.
Adjust the pressure down until you have a stream of 2cm flames.
The speaker is then activated, and when you hot the resonant frequencies, you see the appropriate series of crests in the flame heights.
I could never get the fundamental, and had difficulty with the 1st overtone, but the next 5 overtones were easily achieved and observed.
The flames look like a perfect model of the pipe open at each end - although it is actually closed at both ends. This is due to the way the flames are produced. The antinodes are regions where the gas pressure is varying widely, resulting in an unstable/absent flame, while the nodes are where the pressure is basically constant, giving a steady flame.
The standing waves are formed in hot gas (the tube is full of gas and soon gets hot), so by measuring the wavelength (use a meter rule and measure the distance from node to node (and double)) and the frequency you can calculate the speed of sound - and it is NOT 330 m/s.
I used a Brass pipe approx 5cm (2") in diameter and 90cm (3') long.

The following youtube video is of someone using a longer pipe.

 

[MatthijsRog]

Thanks for the help!

I did a quick experiment yesterdat with a speaker outputting a fixed-frequency sine in front of a hollow open-ended cylinder with a moveable endpiece. The speaker was set up about two centimetres before the tube, and the whole thing resonated like an open-open cylinder.

Also, thanks for the video of the demonstration! I think I'll be trying to build the same thing for my students, but with styrofoam balls instead of flaming gas--I'm pretty sure the faculty doesn't allow me to play with fire :p

 

[PeterO]

Thanks for the help!

I did a quick experiment yesterdat with a speaker outputting a fixed-frequency sine in front of a hollow open-ended cylinder with a moveable endpiece. The speaker was set up about two centimetres before the tube, and the whole thing resonated like an open-open cylinder.

Also, thanks for the video of the demonstration! I think I'll be trying to build the same thing for my students, but with styrofoam balls instead of flaming gas--I'm pretty sure the faculty doesn't allow me to play with fire :p

Fire is so much more fun - and leaves a more lasting impression! It also provides a method of measuring the speed of sound in something other than air. (though I have always dreamed of setting up your equipment in a tub filled with Carbon Dioxide to measure the speed of sound in that medium.

 

[anorlunda]

I think I'll be trying to build the same thing for my students, but with styrofoam balls instead of flaming gas--I'm pretty sure the faculty doesn't allow me to play with fire :p

Wouldn't it be equally effective teaching to show that Rubens' Flame video?

 

[PeterO]

Wouldn't it be equally effective teaching to show that Rubens' Flame video?

That particular video is quite confusing. Often times it sounds like a square wave is being used - and thus a mix of frequencies. As the frequency reduces, you can expect to see fewer and fewer peaks - with the distance between them growing - but that is not the case.
It does show the effect we are after, but the results look wierd.

 

[MatthijsRog]

Wouldn't it be equally effective teaching to show that Rubens' Flame video?

Sorry for the time delay, I must've missed the alerts. Still wanted to reply, though.

The course I (help) teach is a course in experimental physics. Thus, showing videos is a little off limits. In general, I would always prefer letting students do a project on a subject (if time allows and it is sufficiently serious) instead of watching videos, because it sticks with them much better and it helps build very useful skills.

Which also explains why I won't let them build a Ruben's tube, even though the thought of it makes my mouth water. Lab safety first :-) The faculty doesn't allow us to let students play around with flaming gasses, which is a pity.

 

[ZapperZ]

I'm a bit puzzled by this whole thread. I believe that you are trying to do an experiment that is similar to this one:

http://media.uws.ac.uk/~davison/labpage/tube/tube.html

So I am not sure what the complications are here, because it appears to be straight-forward. If you use frequencies in the audible range, you can hear an amplification of the sound at the resonant frequencies.

BTW, the open end where the speaker is not considered as a "closed" end. That end is the antinode at resonance.

Zz.

 

[MatthijsRog]

You are completely right. Had I found that website, I would've known.

However, since the practical will be taught for the first time, we have no real indication of whether things will "work". The first question I asked to prevent myself from wasting time--in the second post I explained that I ended up trying it out anyway and discovering that it was an open-open end cylinder.

As for the second question, I haven't been able to answer it myself, but due to the low transmission of sound waves on most materials, it doesn't seem too promising.