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How to calculate the Qtc into inches on a guitar cabinet?

quot;Guitar Cabinets: Sealed (or acoustic suspension)

Sealed guitar cabinets are the main staples of the 4x12quot; stack cabinet manufactures like Fender and Marshall (what guitar player doesn't want a full stack?). Sealed enclosures can (in general) handle more power, decrease the frequency response (due to a natural built-in rolloff), and increase the design time.

Sealed enclosures are designed by selecting an overall speaker and cabinet Q (called Qtc in the ****ason book). The concept of a system Q should be familiar to anyone who has studied electronics and filtering theory. Q can be thought of as an overall system response, accounting for resonance of the system. In general, systems with a low Q can recover from resonance quickly, and the response deviation band is fairly narrow. In terms of audio properties, lower Qtc values can respond to transient signals better (or more appropriately they have better transient response), at the cost of slightly reduce power handling capabilities. As the Qtc is increased, overall low frequency output power is increased, along with increased power handling abilities.

From my own experimentation, lower Q values have a cleaner tone, whereas higher values result in a darker and warmer tone. For guitar cabinets, good values of Qtc are between 0.707 and 1.0. Anything below 0.707 lacks the punch in the midrange tones, and anything above 1.0 lacks detail and adds a ~2db response step in the low-mid range, which will have to be corrected with external EQ.

Once an overall system Qtc is selected, you can find the necessary volumes using the equations in ****ason's book. When doing guitar cabinets, try and select speakers with appropriate Qts values that will put the F3 below the lowest fundamental tone produced by the instrument you are playing. For 6 string guitar, lowest fundamental is the low E string that vibrates at 81 Hz. If your F3 is below this then you won't experience low end rolloff in the frequency range of your instrument. Careful examination of the equations reveals that in order to get lower F3's, you'll need to find drivers with the lowest possible Qts. Again, you must juggle all of these parameters and decide what is most important.

As a case in point: I was asked to design a full stack for the guitarist in a heavy metal band. I asked him about his preferred requirements, and all I got was quot;make it damn loudquot;. I also inquired as to what key he played in, and the answer was mostly dropped D.

As a translation into design parameters, he's probably looking for more bass output and power handling: this means a higher Qtc is in order. The F3 should be below the lowest fundamental, which in this case is about 73 Hz(low D). I also had an idea to try and get the response peak to be in line with the D power chord. In this case, I try and make the Fc (or box resonance frequency) at the lower A string (or about 110 Hz). I ended up selecting a Qtc of 1.0. As a side, note, I managed to build these cabinets for around $210 a piece, or about $500 for a full stack! An amazing price difference from commercial offerings.

The result was a cabinet stack tailored to the exact needs of the player. The 2.7 dB peak at 110 Hz added a hard punch to the natural 5th of the D power chord, which sounded incredible. These are the kinds of things you can do with your own designs!

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