Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
( )
Thus, 4 dBu converts to 1.228 V.
Now that we have the two voltages, we can compute the decibel difference between
Compute the voltage difference between 0.316 V and 1.228 V:
( *
From this you see that the lower-voltage device needs to be boosted by 12 dB in order to match
the other device. Combining Sound Levels from Multiple Sources
In the last few sections, we’ve been discussing mostly power and voltage decibels. These
decibel computations are relevant to our work because power levels and voltages produce
sounds. But we can’t hear volts and watts. Ultimately, what we want to know is how loud
things sound. Let’s return now to decibels as they measure audible sound levels.
Think about what happens when you add one sound to another in the air or on a wire and
want to know how loud the combined sound is in decibels. In this situation, you can’t just add
the two decibel levels. For example, if you add an 85 dBSPL lawnmower on top of a 110
dBSPL symphony orchestra, how loud is the sound? It isn’t 85 dBSPL + 110 dBSPL = 195
dBSPL. Instead, we derive the sum of decibels and as follows:
Convert to air pressure:
( )
Convert to air pressure:
( )
Sum the air pressure amplitudes and and convert back to dBSPL:
( *
The combined sounds in this case are not perceptibly louder than the louder of the two original
sounds being combined! Inverse Square Law
The last row of Table 4.5 is known as the inverse square law, which states that the intensity of
sound from a point source is proportional to the inverse of the square of the distance r from the
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