Ed's AV Handbook.com
Home Theater & High Fidelity Stereo Audio

Chapter Seven
An Acoustical Strategy
for the small room

Page 2

Batting practice for the audio/video pro and a primer for the novice 

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                               The four acoustical regions of a small room 
          The following initiates with a strategy offered by the 'Master Handbook of Acoustics' that divides the acoustical small room into four regions.  Each region is then matched with a dedicated mix of tactics to cope with acoustical distortion.  It is a mix of well know acoustical principles plus practical solutions garnered from my colleagues over four decades.

Handbook notes for the computations below:

Speed of sound = 1130ft/sec        L = longest room dimension  

Primary mode  =  half the speed of sound    room dimension  

Harmonics of a primary mode = multiples of the primary mode

1. Region of long wavelengths
          The 1st region consists of wavelengths that are longer than the primary room mode of the longest room dimension: more than  565   L .  This region is not affected by small room acoustics.  Some mistakenly believe that this region establishes the lowest frequency a room can reproduce.  That is not true.  In this region the room dimensions simply do not impart any resonant support or affect.

Acoustical tactic for the 1st region
eave this region alone.

2. Region dominated by room modes
          The 2nd region consists of wavelengths shorter than the primary axial mode of the longest dimension but longer than 1.9 feet (the wavelength of 300 Hz).  
Room modes, harmonics, peaks, and nulls.    
          F1 represents the primary axial mode of each opposite room boundary -- height, width, and length. The wavelengths of the 3 primary F1 modes are equal to half the speed of sound divided by its dimension.  
Each of the 3 primary modes produce resonating harmonics.  Their 1st harmonic is F2.  F2 is equal to F1 x 2. The 2nd harmonic F3 is equal to F1 x 3.  The 3rd harmonic F4 is equal to F1 x 4, which is followed by F5, F6,  F7, F8, and so on.  
          The 3 p
rimary aixial modes and their harmonics produce peaks and nulls, acoustical swells, throughout the small room.  

               - F1 peaks at its opposite boundaries;
                  but nulls at the mid-point of the room dimension.
               - F2 peaks at each boundary, and at the mid-point of the dimension;
                  but nulls at the mid-point between each peak.  
               - F3 peaks at each boundary, the middle, and at the and points;
                  but nulls at the mid-point between each peak.

               -  F(x) This peak/null 'swell' behavior continues with each succeeding harmonic.

          From approximately 565L to 300 Hz -- adjacent room modes (includes the spread of all 3 primaries and thier harmonics) with a coincidence or large spacing create distorting peak and null deviations from flat frequency response.  A coincidence is a difference of about 5Hz or less.  Large spacing is approximately 20Hz or more.  
A coincidence creates a peak.  Large spacing creates a dip or null.  Above 300 Hz their influence is minimal. 

Swell management
          Speaker placement influences peaks and nulls.  If a speaker is placed at a room boundary it excites F1 and all of its harmonics.  However if the speaker is placed at the mid-point of the dimension it will only stimulate the even numbered harmonics of F1.   Placed at a third of the dimension -- only the 3rd, 6th, 9th, 11th, etc, harmonics of F1 are stimulated.  Placed at a fourth of the dimension -- only the 4th, 8th, 12th, etc, harmonics of F1 are stimulated; and the pattern continues.  Practical and effective speaker placement will be addressed later in this chapter.

          I have avoided tangential and oblique modes - waves bouncing off more than the two opposite boundaries. Their amplitude is a great deal weaker than primary modes.  Fortunately tangential/oblique modes typically fill in between the more widely spaced primary modes and their harmonics.  Therefore for this 'small room' discussion we will assume that their disruptive affect is negligible.

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Ed's AV Handbook.com
Batting Practice for the AV Pro and a Primer for the Novice.
Copyright 2007 Tux1-598-288   Revised 2018