Page 55 - The Master Handbook Of Acoustics

30 CHAPTER TWO

p 1 = (20 µPa)(12,589)
p 1 = 251,785 µPa
There is another lesson here. The 82 has what is called two signif-
icant figures. The 251,785 has six significant figures and implies a
precision that is not there. Just because the calculator says so doesn’t
make it so! A better answer is 252,000 µPa, or 0.252 Pa.

Logarithmic and
Exponential Forms Compared

The logarithmic and exponential forms are equivalent as can be seen
by glancing again at Table 2-1. In working with decibels it is impera-
tive that a familiarity with this equivalence be firmly grasped.
Let’s say we have a power ratio of 5:

10 log 5 = 6.99 is exactly equivalent to
10
6.99 (2-4)
5 = 10 10

There are two tens in the exponential statement but they come from
different sources as indicated by the arrows. Now let us treat a sound
pressure ratio of 5:

20 log 5 = 13.98
10
13.98 (2-5)
5 = 10 20

Remember that sound-pressure level in air means that the refer-
ence pressure downstairs (p 2 ) in the pressure ratio is 20 µPa. There
are other reference quantities; some of the more commonly used
ones are listed in Table 2-3. In dealing with very large and very
small numbers, you should become familiar with the prefixes of
Table 2-4. These prefixes are nothing more than Greek names for the
powers exponents of 10.