We measure the strength of a sound by its intensity. The intensity is the sound energy crossing unit area in 1 second. It is measured in units of W/m^{2}.The intensity of a sound is proportional to the square of its amplitude.

It is convenient to express sound intensities in terms of multiples of the softest sound that can be heard (about 10^{-12}Wm^{-2}). These ratios get so large that we express them on a logarithmic scale measured in decibels.The Sound Intensity Level (SIL) corresponding to an intensity I is

where the log is taken to the base 10.

Similarly, we compare the strengths of two sounds by finding the ratio of their intensities and expressing the answer in decibels.

The average ear responds to pure tones (sine waves) over a frequency range from about 20Hz to as much as 20,000Hz (20kHz). As we age the higher limit of audibility falls and the effect is more pronounced in men than in women.

The ear responds non-linearly to sound intensity. It is much more sensitive to changes in sound level at low levels of sound than at high levels. On average a ten fold increase in the intensity of a sound makes the sound twice as loud. The ear is much less sensitive to low frequencies than to high frequencies and the effect is particularly pronounced for quiet sounds.

Here is a table of some common ratios and their equivalents in dB

Ratio |
dB |
---|---|

I1 = I2/10 |
-10dB |

I1 = I2/2 |
-3B |

I1 = I2 |
0dB |

I1 = 2×I2 |
+3dB |

I1 = 4×I2 |
+6dB |

I1 = 10×I2 |
+10dB |

I1 = 20×I2 |
+13dB |

I1 = 100×I2 |
+20dB |

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