|MadSci Network: Physics|
There are a lot of variables involved with speaker efficiency, so what you experienced may not always be the case. If I had more specifics on your experiment, I could probably provide a better answer, but I will give the best explanation I can, though I will have to be rather broad. Some things that would have been helpful in providing an explanation would be A. The type of speaker (make and model) B. The size of the speaker C. The dimensions of the box. D. The audio source (constant frequency? Music? Speech? Very important) E. Power source (in RMS and peak wattage, just for an idea of how close the speaker was being pushed to its limit) F. A spectrograph analysis of each case (to show which frequency bands increased in amplitude and which were decreased) It is possible that changes in any of these variables would have altered your outcome, as will become apparent as I continue. Also, you say that the speaker was sealed in the box, but an exact idea of HOW sealed would also be helpful. For instance, you did have to run wires into the box, so whether that was done through a set of connectors which were mounted on one wall of the box or whether that was done by running wires through a hole in the box also makes a difference... Also, was the styrofoam lining mounted very solidly with glue, or was it just kind of placed inside? The results would probably be different between those cases as well. Now, down to the explanation... There are three primary possibilities I see in this case. The first possibility I see is that the styrofoam was acting as a passive radiator. The second is that perhaps you had a hole in the box to run wires through or for some other reason, and the hole was causing the enclosure to act as a Helmholtz resonator. The third is that the conditions inside the box with the styrofoam inside JUST HAPPENED, by chance, to be closer to the conditions that the speaker was designed for (specifically concerning changing pressure conditions). Passive radiation is used in speaker enclosures to increase audio output within a certain frequency range primarily by picking a radiator with specific resonance characteristics. The box is sealed, and, in most cases, the passive radiator is a speaker cone similar to the active speaker, but it is not powered by a magnet or electricity in any form or fashion. The movement of the passive radiator is caused by the sound waves produced by the active speaker and the changing pressure within the enclosure. As the frequency produced by the active speaker nears the resonance of the passive radiator, the passive radiator will begin to resonate and will produce a second sound wave. If the enclosure is properly designed, the two sound waves will be constructive (that is, the peaks of the two waves will coincide, and the troughs of the two waves will coincide so as to produce a total wave which is larger than either of the two original waves). If the enclosure is poorly constructed, the sound wave created by the passive radiator could have a 180 degree phase relation with the primary wave created by the active speaker, and the combination of the two waves will be destructive (that is, the peak from wave 1 coincides with a trough from wave 2, and a peak from wave 2 coincides with a trough from wave 1, so when you add the two waves together, the result is a wave which has a lower amplitude than either of the two original waves). That being said, it is possible that the addition of the styrofoam lining the box caused each surface of the box to resonate at frequencies which the speaker was putting out. Thus, the whole box was acting as a passive radiator, or each face of the box was acting as a passive radiator, and rather than absorbing the sound wave, each face was reradiating that sound wave. Note that this is NOT amplification as you put it, but rather, an increase in efficiency. You cannot create energy, but, you can make things more efficient by keeping the energy from being turned into another kind of energy. With the original plywood box, the box could have been absorbing the sound energy and turning it into thermal energy (heat), while the addition of the styrofoam changed the characteristics of the box so that rather than convert the sound energy into heat, it took the sound energy and reradiated it as another wave of sound energy. OK, so there you have the explanation for the first possibility. The second possibility I see is that maybe there was a hole in the box for the wires or there was an opening in the box because of a mistake in its construction. This could cause the box to act as a Helmholtz resonator (or, should I say, the air within acts as the resonator). The example I see for Helmholtz resonation the most is "It's like when you blow across the top of a bottle." Essentially, a ported speaker enclosure (one with a hole in it) is tuned so that as the air moves in and out of the box through the hole, the changing pressure caused by the air moving in and out sets up a resonant oscillation. The "in and out" movement of air causes a sound wave. "Well, hold on," you might be saying. "The hole did not change in size when the box was lined with styrofoam!" True, but the styrofoam did decrease the volume of the box, and it is also possible that the styrofoam sealed other holes that air may have been escaping from. It is possible that the addition of styrofoam caused the box to be tuned to a frequency which was moreprevalently produced by your speaker. If so, then the box would only begin to act as a Helmholtz resonator in the case with the styrofoam, or perhaps it acts as a Helmholtz resonator in both cases, but it was tuned to a better frequency in the second case. Almost done here... The third case that could have taken place is that the enclosure just happened by chance to be closer to the manufacturer's intentions for the speaker when you lined it with styrofoam. Most speakers are designed to be mounted in the front of a box, where there is a counteracting pressure inside the box to oppose the speaker's movement. As the speaker cone moves inward, the pressure inside the box increases due to the compression of the air inside, and since the pressure on the inside surface of the cone is higher than the pressure on the outside surface of the cone, the net force on the cone caused by the air pressure is outward. The roles are reversed as the cone is forced outward by the electromagnetic field produced by the speaker's voice coil...as the cone is forced out by the voice coil, there is a counteracting force caused by the difference in air pressures inside and outside, and the air pressure forces the cone inward as the voice coil forces the cone outward. Now, I'm not even sure whether the speaker you had inside this box was in its own smaller enclosure or not, but assuming that it was not in a second smaller enclosure, you essentially had it in a "free-air" situation where there were no opposing forces caused by air pressure. The speaker probably was not designed for that, and it may not have been operating correctly because of this. When the styrofoam was put inside, you may have reduced the volume of the box enough to make it less like the open environment, or perhaps the proximity of the speaker's cone face to a wall of styrofoam allowed for an increased pressure on the face of the cone, allowing for less of a free-air environment. Normally, the free-air situation will be more efficient, but if you were playing music which was complex, perhaps the speaker was not operating well at all in this free-air situation. If I had to guess as to which of these situations is most likely to be the root cause, I'd have to go with scenario one, followed by two, then three. Resonance of the enclosure is most likely the cause. If you decide to revisit this experiment, you can draw better conclusions by having very specific and accurate data. I would suggest using a very controlled power source, and also a very controlled audio source. Do not use music as your source, as the speaker may not even be able to accurately reproduce multiple frequencies at once. Rather, use a wave generator as the audio source which will allow you to control the frequencies very precisely. You can do a sweep from 20 hz to 20 khz (provided you have speakers which can produce these frequencies) and record the audio output not just in decibels, but rather in a spectrograph-like form. If you are feeding the speaker a 500hz frequency, but the output which you are getting shows a peak at 500hz AND another wave at 250hz, you may be getting harmonic resonance, and that would be important to note. It would also be important to have a third "control" situation where the speaker is not inside a box at all. That way, you can compare all other results to the control result, rather than comparing experimental results to each other. Perhaps you did this and did not mention it, but if you decide to redo this experiment, this is pretty important. You need a control situation that is as untampered with as possible. Also, it would be a good idea to use a microphone that has very flat, accurate, and wide frequency response. Cheap microphones pick up better in the midrange frequencies, and may not pick up below 100hz or above 12khz at all. The best results will be obtained using studio condenser microphones which have extremely flat and accurate frequency response across the whole hearing spectrum. If you used a cheap microphone, you may have been missing out on something important. It would also be good to be in a room which has sound absorbing foam on the walls and ceiling and has a carpeted floor, but I doubt you have access to such a room. I certainly do not. But you would get poor results if you chose something like a gym or a room with tile floor and painted concrete walls. The reverberation within the room would skew your results for sure. Here are some links which I think will be helpful. Helmholtz resonance: http://www.phys.unsw.edu.au/jw/Helmholtz.html Wave addition: http://www.udel.edu/idsardi/sinewave/sinewave.html (try setting the two waves to be exactly the same, but only change the phase relation. This would be relevant to the discussion) Speaker enclosures: http://electronics.howstuffworks.com/speaker9.htm (sorry, its the most reliable source I have on enclosures, but from what I see, the information is accurate) If I come across any more relevant information, I will come back and post more. I hope this helps your total understanding of the subject! sincerely, Joel
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