I. What is the absolute power of a sound with the following intensity levels?
1. 60 dB IL
 X 
 X 
60 = 10 log  12   (implies) 6 = log  12   106 =
 10 
 10 
-6
-12
-6
 (Therefore) X = 10  10 = 10 w/m2
2. 70 dB IL
10-5 w/m2
3. 80 dB IL
10-4 w/m2
4. 110 dB IL
10-1 w/m2
 X 
 12 
 10 
II. What is the absolute pressure of a sound with the following sound pressure levels?
1. 60 dB SPL
2  104 μPa
or
20  103 μPa
2. 70 dB SPL
2  104.5 μPa or
20  103.5 μPa
3. 80 dB SPL
2  105 μPa
or
20  104 μPa
4. 110 dB SPL
2  106.5 μPa
or
20  105.5 μPa
COMBINING EQUAL INTENSITIES FROM DIFFERENT SOURCES
III. Two sounds A and B have the same intensity of 60 dB IL. When these two sounds are presented
together, what is the resulting overall intensity? **
HINT: You cannot add decibel values directly since they are relative values. Hence, the answer to this
question is NOT 120 dB IL. You will first need to convert dB to absolute power units, and then work
through the problem.
Solution
In this case, each sound has the same intensity of 60 dB IL. 60 dB IL corresponds to an absolute
power of 10-6 w/m2. Combining absolute powers for both sounds, the total absolute power is 2 
10-6 w/m2. Converting this back into dB IL, the total intensity is 63 dB IL.
 2  10 6 
 = 10 log 2  10 6  = 10 (log 2 + log 106) = 10 (0.3 + 6) = 6.3  10 = 63 dB IL
Steps: 10 log 
12 
 10

IV. What would be overall resulting intensity of these two sounds when expressed in dB SPL? ****
HINT: Remember the relation p2 ∞ I . Therefore when power is doubled/increased by a factor of
2, pressure only increases by a factor of 2 = 1.414.
Solution
The absolute pressure corresponding to 60 dB SPL is 2  104 μPa. So the new (combined power) is
1.414  2  104 μPa. Using this in the formula,
 1.414  2  10 4
New SPL = 20 log 
2  10

63 dB SPL

 = 20 log (1.414  103) = 20 (log 1.414 + log103) = 20 (0.15 + 3) =

V. If the absolute power is doubled, what is the resulting increase in dB IL? 3 dB
VI. If the absolute pressure is doubled, what is the resulting increase in dB SPL? 6 dB
COMBINING UNEQUAL INTENSITIES FROM DIFFERENT SOURCES
VII.
Two sounds A and B have intensities of 90 dB IL and 80 dB IL, respectively. If these two
sounds are produced simultaneously, what is the combined intensity in dB IL? **
HINT: Convert each to absolute power, add the absolute powers, and then convert it back to dB IL.
Solution
Absolute power of A is 10-3 and that of B is 10-4 w/m2. The combined absolute power is 10-3 + 10-4 =
 11  10 4 

0.001 + 0.0001 = 0.0011 = 11 x 10-4. Using this value in the formula, the new dB IL = 10 log 
12
10


= 90.4
(log 11 = 1.04)