![]() The sound intensity in decibels above the standard threshold of hearing is calculated as a logarithm. ![]() The logarithm to the base 10 used in this expression is just the power of 10 of the quantity in brackets according to the basic definition of the logarithm: The decibel scale is a reflection of the logarithmic response of the human ear to changes in sound intensity: The unit is based on powers of 10 to give a manageable range of numbers to encompass the wide range of the human hearing response, from the standard threshold of hearing at 1000 Hz to the threshold of pain at some ten trillion times that intensity.Īnother consideration which prompts the use of powers of 10 for sound measurement is the rule of thumb for loudness: it takes about 10 times the intensity to sound twice as loud. The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because about 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear.ĭecibels provide a relative measure of sound intensity. Example: If I = 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 10 4, the power of ten is 4, and the intensity is 40 dB: The logarithm involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. Plots on paper with one log scale can show up exponential laws, and on log-log paper power laws, as straight lines (see semilog graph, log-log graph).The sound intensity I may be expressed in decibels above the standard threshold of hearing I 0. Logarithmic graph paper, before the advent of computer graphics, was a basic scientific tool. The geometric mean of two numbers is midway between the numbers. On a logarithmic scale an equal difference in order of magnitude is represented by an equal distance. A slide rule has logarithmic scales, and nomograms often employ logarithmic scales. log( x) from the point marked with the number 1.stellar magnitude scale for brightness of stars Ī logarithmic scale is also a graphical scale on one or both sides of a graph where a number x is printed at a distance c.Some logarithmic scales were designed such that large values (or ratios) of the underlying quantity correspond to small values of the logarithmic measure. Particle size distribution curves of soil.rating low probabilities by the number of 'nines' in the decimal expansion of the probability of their not happening: for example, a system which will fail with a probability of 10 −5 is 99.999% reliable: "five nines".counting f-stops for ratios of photographic exposure.bel and decibel and neper for acoustic power (loudness) and electric power.Richter magnitude scale and moment magnitude scale (MMS) for strength of earthquakes and movement in the earth.On most logarithmic scales, small multiples (or ratios) of the underlying quantity correspond to small (possibly negative) values of the logarithmic measure. In particular, our sense of hearing perceives equal multiples of frequencies as equal differences in pitch. ![]() That makes logarithmic scales for these input quantities especially appropriate. Some of our senses operate in a logarithmic fashion (multiplying the actual input strength adds a constant to the perceived signal strength, see: Stevens' power law). The logarithmic scale can be helpful when the data cover a large range of values – the logarithm reduces this to a more manageable range. The two logarithmic scales of a slide rule Logarithmic scales are also used in slide rules for multiplying or dividing numbers by adding or subtracting lengths on the scales. The value of each mark on the scale is the value at the previous mark multiplied by a constant. It is based on orders of magnitude, rather than a standard linear scale. Common uses include earthquake strength, sound loudness, light intensity, spreading rates of epidemics, and pH of solutions. A log scale makes it easy to compare values that cover a large range, such as in this mapĪ logarithmic scale is a scale used when there is a large range of quantities. ![]()
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