Topic 2
Sound intensity is the power per square meter carried by a sound wave, often measured in decibels.
  • Power – the amount of energy per unit time. The units of power are watts = joules per second.
  • Energy is usually measured in such units as joules (kg · m2/s2), ergs, calories or kilocalories.
  • Sound intensity is measured in watts per square meter, or W/m2.

The threshold of hearing is the quietest sound detectable by the human ear. This value obviously varies between individuals, but the accepted value is 1 x 10-12(W/m2).

The greatest sound intensity that can be experienced before feeling the sensation of pain is known as the threshold of pain. The commonly accepted value for the threshold of pain is 1 (W/m2).

Note that the range in sound intensity between these two thresholds spans twelve orders of magnitude. Because this range is so large, a different system of measurement is often used for convenience. Sound intensities are scaled by factors of ten using what is called a logarithmic scale. Each unit change on this scale represents a factor of ten change in sound intensity. The units given to this new scale are bels, named after Alexander Graham Bell. This scale is referred to as the sound intensity level and the reference point for beginning this scale is the threshold of hearing.

10-12 W/m2  =  0 bel

10 times that intensity is 10-11 W/m2  =   1 bel

Because each interval on this scale represents such a large increase in sound intensity, a finer scale in which bels are divided into decibels (dB) is often the most convenient.

1 bel  =  10 decibels

1 decibel  =  1dB  =  (1 bel)/10
Thus, 10 dB is 10 times as intense as 0 dB.

20 dB is 100 (or 102) times as intense as 0 dB.

30 dB is 1000 (or 103) times as intense as 0 dB.

60 dB is 1,000,000 (or 106) times as intense as 0 dB.

= 10 x 10-12 W/m2 = 10-11 W/m2

= 102 x 10-12 W/m2 = 10-10 W/m2

= 103 x 10-12 W/m2 = 10-9 W/m2

= 106 x 10-12 W/m2 = 10-6 W/m2
Here are some sound intensities and the corresponding intensity levels encountered in daily life
Sound Intensity (W/m2) Sound Level (dB)
A Whisper 10-10 20
Normal Conversation 10-6 60
Loud Music 10-1 110
A Siren (nearby) 1 120
A Jet Airplane (nearby) 102 140
If the intensity of a sound is known, then the sound intensity level, in decibels, can be determined from the expression

b = 10 log(I/I0)

where I0 is the threshold of hearing, and I is the intensity of the sound.

If the sound intensities of two sounds are known, then the difference in sound intensity level between the two sounds is given by the expression

b 21 = 10 log(I2/I1)

where I1 and I2 are the intensities of the sounds, with I2 being the sound of greater intensity.

Sound intensity is an objective physical quantity.

Loudness is a subjective physiological sensation associated with hearing sounds of different intensities.

Our ears sense some frequencies better than others because our eardrums vibrate more efficiently at some frequencies than others. This is why a 3500 Hz tone at 80 dB sounds twice as "loud" as a 125 Hz tone at 80 dB (to most people). Humans are the most sensitive to tones near 3500 Hz.

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