# Small room acoustics for recording or theater playback

A typical small recording room is going to be made in a room available in the home. There are magnified acoustical issues with small rooms that are not issues at all with medium to large rooms, rooms of 1500 cubic feet or larger.

Let us use a room of the dimensions, 12 feet in length, 10 feet in width and 8 feet in height.

The first thing we want to do is to understand how sound is going to be in this room, how it is going to interact with the space as sound becomes the small room acoustics.

Each Frequency has a known length, that means that ever note that you can play, you can determine mathematically how long in feet and inches is the frequency in question.

The simple equation is: 1130 / (measurement in question) / 2= f
The speed of sound is 1130 feet per second.
The “measurement in question” is the length or width or the height of the room in question.

And f is the frequency that presents the issue.

What is the issue?

The issue is that the boundaries of a room present modes also known as standing waves. This is the point in the room where a frequency will seem louder and distort the listeners ability to make valid judgment.

These are our points of interest that will need treatment or require setup of listening position knowing what it is the room presents to us as a listener at the mix position.

Let’s look into the axial modes of a small room 12 feet in length, 10 feet wide and 8 feet in height.

Using only the axial modes we can get an understanding of how complex the sound field will be in this room, which aids in the task of making a more sonically pleasing environment.

1130/12(L)=94.17 Hz /2=47.1Hz (1,0,0)
1130/10(W)=113 Hz /2=56.5Hz (0,1,0)
1130/8(H)=141.25 Hz /2=70.62Hz (0,0,1)

Below 47.1Hz there is no modal support, this means that every frequency below 47.1Hz the room is basically invisible and you have no control of this frequency region.

To continue, we will define all the axial modes in the L,W,H dimensions up to 300Hz.

To do this take each individual frequency, starting at the (L)ength and add the defined frequency to itself, keeping a written record of each resultant number until you get to 300Hz (+/-).

```Length Frequency WaveLength
L=47.1 47.1 24feet(1,0,0) 47.1+47.1=94.2
94.2 12feet(2,0,0) 94.2+47.1=141.3
141.3 8feet(3,0,0) 141.3+47.1=188.4
188.4 6feet(4,0,0) 188.4+47.1=235.5
235.5 4feet 10inches(5,0,0)
235.5+47.1=282.6
282.6 4feet(6,0,0)

Width Frequency WaveLength
W=56.5 56.5 20feet(0,1,0)
56.5+56.5=113
113 10feet(0,2,0)
113+56.5=169.5
169.5 6feet 8inches(0,3,0)
169.5+56.5=226
226 5feet(0,4,0)
226+56.5=282.5
282.5 4feet(0,5,0)

Height Frequency WaveLength
H=70.62 70.62 16feet(0,0,1)
70.62+70.62=141.24
141.24 8feet(0,0,2)
141.24+70.62=211.86
211.86 5feet 4inches(0,0,3)
211.86+70.62=282.48282.48 4feet(0,0,4)
```

These are the problem areas that the room presents in the form of axial modes.

There is an unfortunate area of this room where the axial modes are reinforced.

L,W,H mode(3,0,2): The frequency of 141.3 found in the length of the room and 141.24 found in the height of the room is one area of concern.

L,W,H mode(6,5,4): The frequency of 282.6, 282.5 and 282.48 are all present in the length, width and height respectively. The above graphic is a demonstration of how and where the Axial modes line up in this room.

```Red    lines=Axial Mode 2
Yellow lines=Axial Mode 3
Blue   lines=Axial Mode 4
Black  lines=Axial Mode 5
Green  lines=Axial Mode 6
```

In the above graph of this room you see that axial mode 3 and axial mode 6 in the length measurement of the room are right on top of each other!

Not to leave any stone unturned, there is one more measurement that is the longest of either of the length, width or height and that is the distance from the top corner of the room to the bottom cross corner. This distance is 17 feet 6 5/8 of an inch and represents an oblique mode. The frequency associated with this distance is 32.2 Hz .

Nuances of frequency crossover are to be expected. With this fourth measurement we have yet another frequency added to the mix, sonically and literally.

And if cross over is to be expected we are not let down. Like a musical network of handholding, this 32.2Hz frequency interacts with the mode 2 frequency of 94.2Hz (32.2 X 3 = 96.6Hz) that is found in the (Length) of the room.

32.3Hz X 7 = 225.4Hz and that is a match for the mode 4 frequency of 226Hz that corresponds with the (Width) measurement. That is a close hit musically speaking.