Audio Engineering

60 Chapter 2

Example
A loudspeaker has a sensitivity of LP  99 dB at 4 ft with 1 W of input power. What will
the level be at 100 ft?

1. 
   

   Find the relative dB for 4 ft (relative dB  12 dB).

   
   


2. 
   

   Find the relative dB for 100 ft (relative dB  40 dB).

   
   


3. 
   

   Calculate the absolute dB (40 dB – 12 dB  28 dB).

   
   


4. 
   

   LP  9 9 d B – 2 8 d B  71 dB.

   
   

Example
If we raise the voltage from 2 to 10 V, how many decibels would we increase the power?

1. Find the relative dB for a ratio of 2 (relative dB  6 dB).


2. Find the relative dB for a ratio of 10 (relative dB  20 dB).


3. Absolute dB change  2 0 d B – 6 d B  14 dB.


4. Because a dB is a dB, the power also changed by 14 dB.

2.16 Finding the Logarithm of a Number to Any Base ...................................................

In communication theory, the base 2 is used. Occasionally, other bases are chosen. To fi nd
the logarithm of a number to any possible given base, write

xb n (2.35)

where x is the number for which a logarithm is to be found, b is the base, and n is the
logarithm.

Then write

logxn b log (2.36)

a n d

log

log

x

b

n. (2.37)