Measurement 47This effect is commonly called the inverse square law change in level. Gravity, light,
and many other physical effects exhibit this rate of change with varying distance from a
source. Obviously, if you halve the radius, the levels all rise by 6 dB.
2.8 Directivity Factor .....................................................................................................
Finally, make the point source radiating one acoustic watt a hemispherical radiator instead
of an omnidirectional one. Thus at 0.282 m the surface area is now half of what our sphere
had or 0.5 m^2. Therefore our intensity is now 1 W/0.5 m^2 or the equivalent 2 W/m^2 :
10 log
2 W/m
1 W/m3.01 dB.2
2 Therefore our LP is 123.01 dB. Lw remains 120 dB.This 3.01-dB change represents a 2:1
change in the power per unit area; thus, a hemispherical radiator is said to have twice the
directivity factor a spherical radiator has. The directivity factor is identifi ed by a number
of symbols— DF , Q , Rθ , λ , M , etc. Q is the most widely used in the United States so we
have chosen it for this text. Directivity can also be expressed as a solid angle in steradians
orsr 4 π / Q.
2.9 Ohm’s Law
Recall that the use of the term “ decibel ” always implies a power ratio. Power itself is
rarely measured as such. The most common quantity measured is voltage. If in measuring
the voltage of a sine wave signal (oscillators are the most reliable and common of the
test-signal sources) you obtain the rms voltage, you can calculate the average power
developed by using Ohm’s law. Figure 2.5 is a reminder of its many basic forms and uses
the following defi nitions:
W is the average electrical power in watts (W).
I is the rms electrical current in amperes (A).
R is the electrical resistance in ohms ( Ω ).
E is the electromotive force in rms volts (V).
PF is the power factor (cos θ ).