On this sub page, I will prove how important it is for a woofer to be tuned to its speaker cabinet. This is quite a long page with charts and definitions but contains the most important information dealing with speaker design and is well worth your reading. Save it or add a bookmark if you don't have time to read it all. First I will have to clear up some myths and define some terms. I get many calls from the know-it-all types. When they start spouting off about wanting to "improve" their speakers with new woofers and then ramble on about power handling and magnet size, I know I'll have to spend awhile on the phone reeducating them. This page will hopefully save my vocal cords and reduce my phone bill.

First, I must dispel all of these ridiculous notions. Wattage is a measure of power. A 100 watt light bulb puts out much more light than a 40 watt bulb so one might assume that this works the same way with speakers. This is not the case. A light bulb will only draw its rated amount of power and will draw this at all times to put out a constant luminance. Speakers however are given a constantly varying amount of energy. If we put a constant loudness test tone into both a 40 watt and a 100 watt speaker, without knowing anything else, it would be a toss up as to which speaker would be louder. Maybe they would be equally as loud. How loud a speaker will be is not determined by its power handling but by its efficiency.

The voice coil in a speaker is much like a fuse. A fuse conducts electricity just fine until too much current passes through it (which of course then melts the wire). The power of a speaker has to do with the thickness of the voice coil wire (just like a fuse), the number of coil windings, and the diameter of the voice coil former (larger coils dissipate more heat). I've seen speakers with one inch diameter voice coils, stamped frames, and ten ounce magnets labelled as handling 200 watts. It might handle this power for a second or so but then it will melt! Yet, people are buying these things and thinking that they're getting a great bargain and then wondering why their 50 watt receivers are blowing them up. Some manufacturers (usually not the well known brands) lie about their specs to sell more of their products. You'll find these mislabeled speakers at those travelling stereo sales, discount wholesale clubs, and the "wheeler dealers" who sell them off the back of trucks ( I'll sell you this $800 pair of speakers today only for $100). Don't trust all that you read. Physics doesn't lie!

The true measure of a speaker's loudness is its efficiency or Sound Pressure Level (SPL) . This quality factor is rated in deciBels which we'll discuss in a moment. A one watt test tone is injected into a speaker and the resulting sound level (dB SPL) is measured at a distance of one meter (on axis) with a sound level meter. Magnet size is often mistaken as a measure of efficiency and this is often (but not always) true. Efficiency depends on the magnet size, the strength of the magnetic material, how much of this strength is focused into the voice coil gap, and how wide the voice coil gap is. It is much easier for the magnetic flux to jump across a small gap than a larger one (just ask Evil Knieval). On the other hand, a small voice coil gap is much more difficult to make without the speaker parts rubbing so these higher quality woofers are precision machined and use cast steel frames to maintain close tolerances. The size and number of windings on the voice coil, the type of wire utilized (round, flat, hexagonal), the resistance of the wire, and the weight of the cone material all affect a woofer's efficiency.

Unfortunately, neither of the above parameters have anything whatsoever to do with the way that a speaker sounds. A woofer (or low frequency driver) is merely a motor. It is driven by an electrical signal that moves it in and out according to the signals amplitude and polarity. The in and out motion vibrates air molecules and this makes the sound that we hear. A cone type driver needs to be placed in a box to get any sort of bass out of it. The box works as a mechanical amplifier (much the way a paper cheerleader's megaphone can amplify a voice). Any box is better than no box, but the best boxes are tuned to reinforce the vibrations of the woofer, thus making them louder while using much less power. A tuned box will also have a linear (flat) response to all frequencies. This works because of a principle called resonance.

We have all probably at some point blown across the top of a cola bottle and noticed that it produced a sound. We are basically exciting the air in the bottle at the tuned frequency created by the volume of the air (not cola) space. Physicists would call this a helmholtz resonator. The more cola consumed, the lower the pitch will be. Try this test: blow across the top of a half filled cola bottle and note the pitch. Have a friend (who isn't tone deaf) sing this same pitch and hold the bottle an inch from your ear. Now have your friend sing the notes below and above this pitch. The note that the bottle is tuned to will resonate and reinforce the sound at this pitch thus making it louder. You'll also feel the glass vibrate in your hand. An opera singer can break a crystal glass with her voice because she hit the resonant frequency of the crystal --- which is so thin that it shatters.

Mathematicians and physicists have found a way to measure all of the important electrical and mechanical specifications of speakers and have developed mathematical models for speaker and box matching. The most noted for this work are A.N. Thiele and R.H. Small. The Thiele-Small parameters have been incorporated into many computer programs that can show you how different driver and box combinations will sound before any wood is cut. It is beyond the scope of my page to go into this any further but I would highly recommend two books on the subject to anyone wanting more information on this subject (or anything else that I have discussed). Building Speaker Systems and Advanced Speaker Systems (stock number 62-2317) are both available at Radio Shack stores. I also think that they should be required reading for all Radio Shack personnel.

A while back, after refoaming a nice set of JBL studio monitors for a customer, he told me of an old pair of speakers that he was wanting to restore. Chris had built a pair of cabinets in high school wood shop years ago but never could get a decent sound out of them. After telling him all about box tuning he decided to let me find the right speakers for a nominal engineering fee. Before talking to me, he was going to purchase a pair of twelve inch "replacement speakers" that they sold at the local electronics store. After designing his system, I decided to compare my woofer to the one that he almost bought. The results and explanations below are quite astounding.

Usually, I will enter a few of the driver's T-S parameters (Fs, Vas, Qts) into the computer and it will calculate the internal volume of the cabinet and how wide and deep to make the tuned ports. In this case, I had to enter the specifications of about thirty drivers while using the box size as a constant to find the right one. I was searching for the one driver that would would produce the deepest bass frequencies with the flattest possible response in his cabinet. After over an hour of comparing specs, I settled on a very nice woofer. It wasn't near the most expensive one either. In fact, speakers costing three times as much as what I settled on didn't provide as good a response in his cabinet. Also knowing the published specs on the speaker he was about to buy, I decided to compare both of them. I couldn't believe how bad his intended speaker would have sounded!

To understand the chart below, I must introduce you to the deciBel (named after Alexander Graham Bell). It is a way to measure the difference between any two quantities (here we will use it for sound pressure levels). This is a logarithmic scale which compresses very large quantity differences to make them more manageable. On a daily basis, our ears are subjected to levels more quiet than a soft whisper (30dB SPL) to a jet airplane flying directly overhead (130db SPL). This is a difference of 100 dB. Doing the math to convert it back to a ratio, we find that the differences between these two levels is 10,000,000,000 to one! That's ten billion to one. Without getting a math lesson, lets just say that every increase (decrease) of 3 dB is equal to twice (or half) the sound pressure level. Every 6 dB is four times as loud, every 9 dB is eight times as loud, and so on. In interpretation of the table below, I'll give you the exact ratio values.

Okay, back to our reverse engineering. Speaker A (on the left) is the speaker that Chris would have chosen and speaker B is my choice. These measurements are based on a cabinet size of 2.936 cubic feet. As you can see, speaker B has a much flatter response over the entire range with the highest peak being only 1.63 dB (1.45 times as loud as the nominal 0 dB level). Speaker A has a BIG hump in the response from 50 hertz to 110 hertz resulting in a peak of 7.63 dB (5.79 times as loud as the nominal level) at 65 hertz. This means that the "C" note two octaves below middle C (65.41 hertz) will be more than 6.6 times as loud as the "F" note below it (43.65 hertz) if both notes are played at the same level by the musician. Recording engineers would not tolerate this and neither should you. People perceive this as "boomy" or "muddy" bass. NOTE: In case you didn't follow, I used the level of -0.57 dB at 45 hertz (the closest to F) to get the peak of 8.2 dB. Since we are dealing only with box tuning, our chart stops at 200 hz. Frequencies above 200 hertz directly radiate from the speaker cone and do not use the box for reinforcement.

The f3 point (frequency at which woofer response has dropped by 3 dB and starts its natural rolloff) of speaker A is 44.71 hertz even though the speaker's resonant frequency (Fs) is listed as 21.5 hertz. This shows you that a published spec and how deep a speaker will get in your cabinet are often two different things. Speaker B doesn't hit the 3 dB drop until 29.98 hertz. At 35 hertz, speaker B is 6.72 dB (4.69 times) louder than speaker A and at the critical, audiophile surround sound subwoofer earthquake jumbo low frequency of 20 hertz (my definition), it is a whopping 6.09 dB or 4.06 times louder than speaker A.

Pretty impressive, huh? You should already be able to see that speaker A has no earthly business being anywhere near our cabinet. To make things more interesting, there are a few parameters that the chart does not take into account. The deciBels listed on this chart are relative values to determine how flat the frequency response is in the cabinet. These are not the dB SPL values that we mentioned with the jet. Speaker A will produce a sound pressure level of 89 dB (with one watt measured at one meter) versus speaker B's efficiency of 90.16. This makes speaker B 1.16 dB or 1.3 times (30%) louder than speaker A across the entire frequency range. Our new scaled value at 20 hertz would make speaker B 7.25 dB or 5.3 times the loudness level of speaker A at this critical frequency! This means that if speaker B is reproducing a 20 hertz tone at its rated power of 80 watts (109 dB SPL) that speaker A would need an amplifier power of over 400 watts to produce the same sound! The problem here, of course, is that speaker A will blow up at 50 watts!

Speaker A only has a 1.5 inch diameter voice coil versus speaker B's 2 inch (bigger size = more heat dissipation = more power handling) coil. Speaker B only cost Chris $10 more than speaker A would have. Of course, I designed a crossover and sold him mids and tweeters (matched to the woofer's efficiency). His verdict: THESE SPEAKERS NOW SOUND AS GOOD AS HIS JBL STUDIO MONITORS.

The above chart was in no way meant to demean the quality of replacement speaker A. This is done purely to point out the idiotic way in which some companies strive to get your hard earned money. Oh, it would be VERY nice to have such a thing as a general replacement loudspeaker but Father Physics won't allow them under his roof. I estimate your chance of getting any replacement speaker to sound as good as your original did is about one in thirty. The odds increase when you also have to match woofer efficiency to your other drivers --- not to mention that you'll have to replace BOTH speakers to retain stereo imaging. In addition, you'll only get a ninety day warranty and there is the chance that you might destroy them by adding too much bass to compensate for an untuned box!

Anyway, what I would like to point out is that if you were designing your own system and let the computer tell you how big of a cabinet to make, speaker A may be a great choice for your system. To give speaker A a chance at redemption, table 2 contains optimum box enclosure frequency graphs based on the same published T-S parameters as above. In this case, it looks like speaker A wins at 20 hertz by being 3.36 dB (or 2.16 times ) louder (scaled). Please note, however, that speaker A needs an 80 cubic foot box (a cube of 4.3 feet per side --- or the volume of almost six stoves!) while speaker B needs only 5.88 cubic feet ( a cube of 1.8 feet per side) to perform optimally. The power handling and efficiency of each speaker has not changed.

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