LOUDNESS OF SOUND

We use a logarithmic scale when there is a wide range of values, and when the change in a value depends not on the absolute size of the change but on the proportion to the value itself. The same is tone of the decibel scale. There are two reasons why a logarithmic scale is useful:

Quantities of interest exhibit such ranges of variation that a dB scale is more convenient than a linear scale. For example, sound pressure radiated by a submarine may vary by eight orders of magnitude depending on direction.

The human ear interprets changes in loudness within a logarithmic scale. The sensation of loudness of sound is not proportional to the energy intensity, but is rather a logarithmic function. Loudness, in Bels (after Alexander Bell), of a sound of intensity I is defined to be , where is the minimum intensity detectable by the human ear (such as the tick of a watch at 6 m under quiet conditions), . When a sound is 10 times as intense as another one, its loudness is 1 Bel greater. If a sound is 100 times as intense, it is louder by 2 Bells, and so on. A bell is a large unit, so a subunit, a decibel, is usually used. For L in decibels, the formula is as follows:

A sound level meter is the principal instrument for general noise measurement. The indication on a sound level meter indicates the sound pressure, p, as a level referenced to 0,00002 Pa, calibrated on a decibel scale.

Sound Pressure Level =

We can also search for some explanations on the Internet:

http://online.anu.edu.au/ITA/ACAT/drw/PPofM/intensity/Intensity1.html

http://www.point-and-click.com/Campanella_Acoustics/faq/faq.htm#basic_decibel

Based on these explanations, students have to answer various questions about the noise in our environment. So they have to solve various examples of logarithmic equations and not surprisingly, even those who always make remarks about how mathematics is boring, try to find out how much more intensity there is in a rock concert than in whispering to the ear of his/her friend. They also discover if we can simply add up intensity of noise.

The worksheet can be found on

http://rc.fmf.uni-lj.si/matija/logarithm/worksheets/sound.htm