78 Chapter 2
out how many dB down each harmonic is compared to the fundamental, sum up all
the harmonics and then compare their sum to the fundamental value. The difference is
expressed as a percentage. The effi ciency of a loudspeaker in converting electrical energy
to acoustic energy is also expressed as a percentage. We know that
20 log 10 2 0 d b
20 log 100 4 0 d b
20 log 1000 6 0 d b.
Therefore a signal of 20 dB is 1/10 of the fundamental, or 100 1/10 10%.
A signal of 40 dB is 1100 of the fundamental, or 100 1/100 1%. A signal of
60 dB is 11,000 of the fundamental, or 100 1/1000 0.1%. We can now turn this
into an equation for fi nding the percentage when the level difference in decibels is known.
For such ratios as voltage, SPL , and distance:
Percentage
100 1020dB. (2.53)
For power ratios:
Percentage
100 1010dB. (2.54)
Occasionally, we are presented with two percentages and need the decibel difference
between them. For example, two loudspeakers of otherwise identical specifi cations have
differing effi ciencies: one is 0.1% effi cient and the other is 25% effi cient. If the same
wattage is fed to both loudspeakers, what will be the difference in level between them in dB?
Since we are now talking about effi ciency, we are talking about power ratios, not voltage
ratios. We know that
10 log 10 2 0 d b
10 log 100 4 0 d b
10 log 1000 6 0 d b
and so forth.
A 0.1% effi ciency is a power ratio of 1000 to 1, or 30 dB. We also know that 3 dB is
50% of a signal, so 6 dB would be 25%; ( 6) – ( 30) 24 dB. In other words, there