SOUND INTENSITY

One of the amazing features of the human eardrum is its ability to handle an extreme range of intensities of sound waves. We define the intensity of a sound wave as the amount of energy per second being carried by a sound wave through a unit area. In the MKS system of units, this would be the number of joules per second passing through an area of one square meter. Since one joule per second is a unit of power called a watt, the MKS unit for sound intensity is watts per square meter. The human ear is capable of detecting sound intensities as faint as 10 ^{– 12}watts /m², but can also handle intensities as great as 1watt /m² for a short time. This is an astounding range, a factor of 10¹² in relative intensity.

The ear and brain handle this large range of intensities by essentially using a logarithmic scale. Imagine, for example, you are to sit in front of a hi fi set playing a pure tone, and you are told to mark off the volume control in equal steps of loudness. The first mark is where you just barely hear the sound, and the final mark is where the sound just begins to get painful. Suppose you are asked to divide this range of loudness into what you perceive as 12 equal steps. If you then measured the intensity of the sound you would find that the intensity of the sound increased by approximately a factor of 10 after each step. Using the faintest sound you can hear as a standard, you would measure that the sound was 10 times as intense at the end of the first step, 100 times as intense after the second step, 1000 times at the third, and 10¹² times as intense at the final step. The idea that the intensity increases by a factor of 10 for each equal step in loudness is what we mean by the statement that the loudness is based on a logarithmic scale. We take the faintest sound we can hear, an intensity I₀ = 10^{– 12}watts/m² as a basis. At the first setting I = I₀, at the second setting I₁ = 10 I₀ , at the 3rd setting I₂ = 100 I₀ , etc. The factor I/I₀ by which the intensity has increased is thus

...........(1)

Taking the logarithm to the base 10 of these ratios gives

.......(1)