AV Formulas

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Designing, installing, and using AV systems is not always about pretty images and great sound. Because physics plays such an important role in how our systems perform, there are certain mathematical relationships you need to know. Here are some of the most useful and important formulas.

Reverberation Time
T60 Calculates the amount of time it takes for an audible signal to decay 60dB after the source has been turned off. This is the revised Sabine equation.

T60 = 0.05V/Sa

Where:
V is the room volume in cubic feet
S is the surface area of the room boundaries
a is the average absorption coefficient in the room

Critical Distance
Critical distance is the distance from the sound source where the direct sound equals the reverberant sound. Beyond this distance, speech intelligibility may be impaired.

DC = 0.14¬QSa

Where:
Q is the directivity factor of the loudspeaker, on-axis (from manufacturer data sheet)
S is the total surface area of the room
a is the average absorption coefficient in the room

Intelligibility
Based on research measuring literally the percent of "articulation loss of consonants" parts of speech.

%Alcons = 656D22 T602N/QV

Where:
D2 is the distance between the loudspeaker and the farthest listener in feet
T60 is the reverberation time
N represents a factor to account for multiple loudspeakers in a cluster where only one is directly aimed at the farthest listener. (In most simple cases, assume N=1.)
Q is the Q of the loudspeaker
V is total room volume in cubic feet

Inverse Square Law
Calculates the decrease in sound pressure level relative to distance from the sound source.

(Outdoors, where room reflections are not a factor):

Lp1 = Lp - 20logD1/D

Where:
Lp1 is the decreased level at the distant listening position
Lp is the SPL at the original reference distance D
D1 is the distant listening position where you want to know the level

(Indoors, where reverberant field adds to total energy level)

Lp1 = Lp - 20logD1/D + 10log g(D1)/g(D)

Where:
g(x) is given by the following equation:
g(x) = Dc2 + x2
Where x is the distance D1 or D.

Brightness of a display in foot-lamberts

Foot-Lamberts = ANSI lumens of projector / total square footage of screen

Wavelengths
For both sound and light waves, wavelength is calculated using the same formula, except the speed constant (v) is different:

l = v/f

Where:

l is the wavelength
v is the speed
f is the frequency

Speed of Sound
At room temperature (70 degrees Fahrenheit) = 1,130 feet/second, but it's highly dependent on properties of the medium through which the wave is traveling; for example, temperature and humidity.

vsound in air = 1052 + 1.106TF f/s

Where:
TF is Fahrenheit temperature

Speed of Light
In a vacuum, the speed of light is exactly 299,792,458 meters per second. In English units, it's generally rounded off to equal 186,000 miles per second. But like sound waves, the speed of light depends on the material it moves through. For example, light moves slower in glass than in air, and in both cases the speed is less than in a vacuum.

Bandwidth of a video signal
Bandwidth is range of frequencies over which a signal amplitude remains constant as it is passed through a system. Also defined as the difference between the upper and lower limits of a frequency, usually measured in MHz.

BWS = 1/2 [(K x AR x (VLT)2 x FR) x (KH / KV)]

Where:
BWS = Total signal bandwidth
K = Kell factor
AR = Aspect ratio (the width of the display divided by the height of the display)
VLT = Total number of vertical scan lines
FR = Frame rate or refresh rate
KH = Ratio of total horizontal pixels to active pixels
KV = Ratio of total vertical lines to active lines

More to follow.....