“I have a room that measures 11 feet and 6 inchs one way and 11 feet and 6 inchs the other way. It has a ceiling that measures 7 feet and 6 inchs tall. Can I use this as a recording studio mixing room?“
If you want to figure Axial room modes by hand it is a simple equation:
c= The Speed of Sound at sea level is considered to move at a static speed of 1,130 feet per second.
W= The measurement in question.
f = The frequency that correlates to the results of the equation.
Then divide that by 2. Reason being is that you have to make a round trip, from one wall to the other.
Your room has two sets of measurements that will produce the same results, e.g. it is a square room but anyway, 11'-6" looks like 11.5 to a calculator.
1130/11.5=98.26 /2=49.13 or 49Hz
If you do the other wall you get the same results of 49Hz. So these frequencies will support each other meaning that you will get a 49Hz Axial mode from one set of parallel walls and another 49Hz Axial mode from the other set of parallel walls. Two strong and disruptive room modes that support each other and we barely started.
Some will take the “measurement in question” and multiple by two before dividing into “f”, but the results are the same.
For instance, 1130/(11.5X2)=49.13 or 49Hz.
Since we are in this room let’s take a look at the ceiling height 7′-6″ 1130/7.5=150.66 /2=75.33 or 75Hz.
These are the first order Axial Modes,49Hz,49Hz,75Hz. In order to determine other possibilities you have to consider multiples of these frequencies to see if there is continued support or exactly how smooth the room response will be. Will the frequencies be spread out(good) or will they be clumped up(not so good).
If the first order Axial of 49Hz is brought to the third order, 49HzX3, it becomes an third order 147Hz room mode.
Stay with me….
If the first order Axial of 75Hz is brought to the second order, 75HzX2, you get a second order room mode of 150Hz.
You now have a third order 147Hz mode from wall to wall being supported by a second order room mode from floor to ceiling at 150Hz. Only 3 points separate these room modes from being a direct hit, so to speak.
So the square area has proven to be an ineffective area mathematically for our want. Also, this will continue to rule it out in future decisions unless modification of some sort is considered.
You can learn this and more in The Master Handbook of Acoustics