The effect is very much like dropping a stone into a pool of water and causing a ripple pattern (sound waves) extending outwards from the original source (your clapping hands). The particles close to your hands are pushed outwards and bump into neighboring particles, and these then move and bump into more particles.

This effect ripples out and away from your hands as a small group of sound waves. When you clap your hands, you force air particles together and then apart. The particles vibrate back and forth in the direction that the wave travels but do not get carried along with the wave. Sound is a pressure wave caused when something vibrates, making particles bump into each other and then apart. Logarithms are used to compute sound intensity and decibel level “Natural” logarithms (2.The Decibel Scale and Using Logarithms to measure Sound Intensity Base-2 “binary” logarithms (3.322 times larger than common logarithms) are used mainly in computer-related fields. [ Optional additional information about logarithm bases: Any positive number except 1 can be used as a logarithmic base, resulting in logarithms that differ from “common” base-10 logarithms by a ratio equal to the common logarithm of the base chosen.

Music octaves-each one-octave increase in musical pitch means that vibration frequency doubles.

Sound-on the decibel scale, each bel (= 10 decibels) means the sound is 10 times more intense.

Brightness of stars-each increase of 1 in stellar magnitude means a star is 2.51 times dimmer.

pH for acidity/alkalinity-each increase of 1 in pH means 10 times more hydroxyl ions.

Richter scale for earthquakes-each increase of one level means 32 times more energy.

A base of 2 is used in music because notes with a frequency ratio of 2 are harmonious.Įxamples of logarithmic measurement scales The non-10 bases for traditional logarithmic scales are typically those that make the results into convenient numbers (e.g., between 2 and 10 for earthquakes, between 1 and 6 for star brightness). The base of a logarithm does not have to be 10 (although only base-10, or “common”, logarithms are used in this course and in most application areas). The use of logarithmic scales in mathematics and technology is a way of using this same tactic to deal with any range of numerical values where the ratio of the largest to the smallest (the dynamic range) is large. In order to handle this range of input, our senses have evolved so that our perceived response to a stimulus is approximately proportional to the logarithm of its intensity. A whisper is a billion times less intense (in total energy into our ears) than a rock concert. On this scale, the intermediate value of 3.491 (the logarithm of 3,100) can be easily distinguished from both of the other values.

So when using logarithms, the original range from 4,200,000,000 to 0.00025 becomes a compressed range from 9.623 to –3.602. Similarly, the logarithm of 3,100 is about 3.491 and that of 0.00025 is about –3.602 (all numbers between 1 and 0 have negative logarithms). The idea of base-10 logarithms (also called “common” logarithms) carries this idea further by using decimal fractions in the exponents so that the initial number is not needed. The numbers above can be expressed as 4.2×109, 3.1×103, and 2.5×10-4, a style called scientific notation because it is used by scientists who often need to deal with very large or very small numbers. In a regular graph of such a dataset, there is no scale that will show the data well-either the biggest number will be far off the scale at the top, or the middle number (which is less than a millionth of the big number) will be at the bottom and indistinguishable from the smallest number even though it is more than ten million times bigger. Thus the same dataset might contain the relatively big value 4,200,000,000, the intermediate one 3,100, and the relatively small one 0.00025. In chemistry, concentrations of hydroxyl ion can vary by more than 100 trillion times between strong alkalis and strong acids. An example is the energy released in earthquakes - there is a 100-billion-times difference between the energy of the smallest earthquake that a seismograph can measure and the largest ones that occur. Many types of measurements cover an extremely wide range of values. Section 2: Compressing the range of values by using logarithms

Log base of decibel scale