Relative Intensity Is a Ratio of Intensity to Some Reference Intensity
Relative Intensity
Relative intensity is a ratio of intensity to some reference intensity.
Example: The intensity of sound in your ear might be 1 x 10-10 W/m2 but we often compare this intensity
to the least intense sound that the human ear can just detect, called the threshold of hearing
(Io = 1 x 10-12 W/m2).
Therefore Relative Intensity = I / Io = 10-10 / 10-12 = 102 = 100
Relative intensity is often expressed using the decibel scale named after Alexander Graham Bell who wanted to standardize sound intensity values.
Threshold of Hearing = 0 dB Normal Conversation = 62 dB
Vacuum Cleaner = 90 dB Loud Music = 100 dB
Not a linear scale because the human ear can detect a huge range of intensities ( 1 x 10-12 W/m2 to 1 W/m2)
Decibel Math
(I2 / I1) = 10(Db/10) = 10( b2 - b1 /10) where Io = 1 x 10-12 W/m2
(I2 / Io) = 10(b2 /10) I = Intensity of sound (W/m2)
(I2 /I1) is the ratio of two intensities
b = Intensity Level (dB) Db = Difference in Intensity Level (dB)
From this, a ten times as intense a sound corresponds to a change of 10 dB
A change of 10 decibels is perceived by humans as roughly twice as loud
And a two times as intense sound corresponds to a change of roughly 3 dB
(I2 / I1) = 2(Db/3) (approximate method)
How many more times intense is a 6dB difference in intensity level between two sounds?
(I2 / I1) = 2(6/3) = about 4 or (I2 / I1) = 10(6/10) = 4
Example 1:
If the difference in intensity level between two sounds is 40 dB, how many times more intense is the louder sound?
40 dB = 10dB + 10dB + 10dB + 10dB
I2 = (10 x 10 x 10 x 10) I1
I2 = 104 I1
Note: Can rearrange Db = 10 log10 (I2 /I1)
(I2 / I1) = 10(Db/10) = 10(40/10) = 104
Example 2:
The sound level reading in a factory with 10 machines running is 82 dB. If more machines are added so that now the intensity level is 88dB, approximately how many machines are running?
Db = 88 dB – 82 dB = 6dB Every 3 dB corresponds to twice the intensity (so twice the
number of machines)
so…….. a 6 dB differe1/nce = 3 dB + 3 dB
so…. # machines = ( 2 x 2) 10 machines
# machines = 40 machines
Example 3:
Standing 20m from a military jet on takeoff the intensity is 102 W/m2
a) What is the intensity level (dB) at this distance?
b) What is the intensity (W/m2) twice as far away?
c) What the intensity level (dB) twice as far away?
a) (I2 / Io) = 10(b2 /10) (102 / 10-12 ) = 1014 = 10(b2 /10) 14 = b2 /10 b2 = 140 dB
b) I a 1/ r2 (spherical wave) therefore I2 = (1/22)100 W/m2 = (1/4)100 W/m2 = 25 W/m2
c) I2 = I1 (1/4) = I1 x ½ x ½
A change of x2 (or ½) corresponds to +3 dB (or -3 dB)
b2 = b1 - 3 dB - 3dB = 140 dB – 6 dB = 134 dB