How many times more intense is

the sound for the man than for

the woman?

Sound for man is 4 times as intense

16.5 - Sound level in decibels

Sound level: A scale for measuring the

perceived intensity of sounds.

To compare the intensity of two sounds, you could directly calculate the ratio of their

intensities. However, humans do not perceive a sound with twice the intensity as being

twice as loud, so a different system may be used. Loudness is subjective, and having

an objective measurement that corresponds to human perception is convenient. This

measurement is called the sound level (or sometimes, more confusingly, the intensity

level).

The human ear is sensitive to an extraordinary range of sound intensities; at the

extremes, humans can perceive sounds whose intensities differ by a factor of

1,000,000,000,000. Although they can hear a broad range of intensities, people do not

distinguish between them finely. For instance, the human ear cannot very well

distinguish a sound that has an intensity of 1.0 W/m^2 from one with an intensity of

0.50 W/m^2.

To reflect humans’ perception of differences in sound intensity, scientists use a

logarithmic scale. The common unit for the sound level is the decibel (dB), or one-tenth of a “bel,” a unit named after Alexander Graham Bell. A

logarithmic scale provides an appropriate tool for describing the human perception of sounds.

In calculating a sound levelȕ, you start by dividing the intensity of the sound being measured by a reference sound intensity that approximates

the lowest intensity humans can hear. This reference intensity is 1×10í^12 W/m^2. Then you calculate the common logarithm (to the base 10) of

this ratio, which gives the sound level in bels, and finally you multiply that value by 10 to express the level in decibels. This is the first equation

shown to the right.

To practice calculating sound levels in decibels, consider a sound with an intensity of 1.5×10í^11 W/m^2. It has 15 times the sound intensity of

the reference intensity of 1×10í^12 W/m^2. The base-10 logarithm of 15 is 1.2. Multiplying this value by 10 decibels yields a sound level of 12

decibels. A sound level increase of 10 dB means the intensity increases by a factor of 10. In calculations of sound levels, both the numbers

1×10í^12 W/m^2 and 10 (decibels) are considered exact.

You may note that the reference intensity of 1×10í^12 W/m^2 corresponds to a decibel reading of zero. At zero decibels, a human ear can still

barely hear sound. The pressure exerted by this sound is very, very slight: It displaces particles of air by about one hundred-billionth of a meter.

It is possible to have negative decibel sounds, perturbations in air pressure so slight the human ear cannot detect them.

Tests indicate that a one to three decibel change in sound level is about the smallest change most humans can perceive. A general rule of

thumb is that a human will perceive a tenfold increase in intensity as sounding twice as loud. A 50 dB sound is 10 times more intense than a

40 dB sound í remember, it is a logarithmic scale í and a typical human would say it sounds twice as loud.

Sound level

Used to measure perceived loudness

·Units: decibels (dB)

·Logarithmic scale (20 dB is ten times

more intense than 10 dB)

(^312) Copyright Kinetic Books Co. 2000-2007 Chapter 16