The sound level equation can be recast in terms of sound power, as shown in the
second equation to the right. If you know the relative power of two sound sources, you
can use this equation to compare their relative loudness to the human ear, provided the
listener is equidistant from the two sound sources. The reference power P 0 in this
equation is the power at the source that results in the reference intensity at the location
of interest. For instance, you might determine this value for a loudspeaker for an
audience member 75 meters away.
ȕ = sound level
I = intensity of sound
reference intensity I 0 = 1×10í^12 W/m^2
P = sound power of source
P 0 = reference sound power
Units: decibels (dB)
16.6 - Sample problem: sound level
Assume the sound power of the loudspeakers equals the power supplied by the stereo.
Variables
What is the strategy?
- State two equations that relate sound level to power, for both the current system and the proposed system.
- Subtract the two equations and solve the resulting equation to determine the power of the new stereo.
Sitting on a sofa, your roommate
hears 100 dB from your stereo, which
supplies 10 W to each speaker. He
says this is lame and requests a
system with a maximum 120 dB. How
many watts of power should the new
stereo supply to each speaker?
current power per speaker P 1 = 10 W
reference power level P 0
current sound level ȕ 1 = 100 dB
proposed power per speaker P 2
proposed sound level ȕ 2 = 120 dB