There are two important
characteristics of sound or noise - frequency and loudness.

Frequency of Sound

Sound is the quickly varying pressure wave travelling through a medium. When sound travels through air, the atmospheric pressure varies periodically. The number of pressure variations per second is called the frequency of sound, and is measured in Hertz (Hz) which is defined as cycles per second.

The higher the frequency, the more high-pitched a sound is perceived. The sounds produced by drums have much lower frequencies than those produced by a whistle, as shown in the following diagrams. Please click on the demo button to hear their sounds and the difference in pitch.

Loudness and the Decibel Scale

Another property of sound
or noise is its loudness. A loud noise usually has a larger
pressure variation and a weak one has smaller pressure
variation. Pressure and pressure variations are expressed
in Pascal, abbreviated as Pa, which is defined as N/m^{2}(Newton
per square metre).

Human ear can perceive
a very wide range of sound pressure. The softest sound
a normal human ear can detect has a pressure variation of 20
micro Pascals, abbreviated as µPa, which is 20
x 10^{-6} Pa ("20 millionth of a Pascal") and is called the Threshold of Hearing. On
the other hand, the sound pressure close to some very
noisy events such as launching of the space shuttle
can produce a large pressure variation at a short distance
of approximately 2000 Pa or 2 x 10^{9} µPa.
The following table illustrates sound pressure level
of the above events expressed in Pa and µPa.

Sound
Pressure expressed in

Pa

µPa

Softest
Noise just Heard by a Human Ear

20
x 10^{-6}

20

Launching
of the Space Shuttle

2,000

2
x 10^{9}

To express sound or noise in terms of Pa is quite inconvenient because we have to deal with numbers from as small as 20 to as big as 2,000,000,000.

The following table shows some common sound or noise in terms of µPa:

Source
of Sound/Noise

Approximate
Sound Pressure
in µPa

Launching
of the Space Shuttle

2,000,000,000

Full
Symphony Orchestra

2,000,000

Diesel
Freight Train at High Speed at 25 m

200,000

Normal
Conversation

20,000

Soft
Whispering at 2 m in Library

2,000

Unoccupied
Broadcast Studio

200

Softest
Sound Human can Hear

20

A simpler way is to use a logarithmic scale for the loudness of sound or noise, using 10 as the base. The following is a brief introduction of the common logarithm to the base 10.

Click on the demo button, you may learn more about the relationship between linear and logarithmic scales.

To avoid expressing
sound or noise in terms of Pa, which could involve
some unmanageable numbers, the decibel or dB scale
is used. The scale uses the hearing threshold of 20
μPa or 20 x 10^{-6} Pa as the reference level.
This is defined as 0 dB.

Sound pressure level, which is often abbreviated as SPL or L_{p}, in decibels (dB), can then be obtained using the following formula. You can click on the demo button to learn the formula.

In the following chart, some sounds are expressed both linearly in µPa and logarithmically in dB. One can see how the logarithmic scale helps us to handle numbers on a wide scale much more easily.

One useful aspect of
the decibel scale is that it gives a much better approximation
to the human perception of relative loudness than
the Pascal scale. This is because human ear responds
to the logarithmic change in level, which corresponds
to the decibel scale.

Adding Sounds or Noises together on the Decibel Scale

In real life, several sources of sounds often occur at the same time. One may be interested to know what results when one sound is combined with another, i.e. the addition of sounds.

Adding 60 apples to 60 apples results in 120 apples. But this is not the case with sounds when they are expressed in decibels. In fact, adding 60 decibels to 60 decibels gives 63 decibels. The following formula explains the general principle of adding sounds on the decibel scale. Please click on the demo button to see the details.

One can use the above formula to add three sounds together - 60 dB, 65 dB and 70 dB. Please click on the demo button to learn how to use the formula to add the three sounds together.

Addition of sound levels can also be done simply using the following chart.

Let us try adding the three sounds of 60 dB, 65 dB and 70 dB by using the chart.

In using the Chart, two sounds are added together first. The resultant sound is then added to a third sound and so on. Please click on the demo button to understand how to add the SPL_{1}, SPL_{2} and SPL_{3} together.

Click on the demo button, you can learn how to add the sound levels using the chart.

The
"A-weighting"

A
normal human ear is able to hear sounds with frequencies
from 20 Hz to 20,000 Hz. The range of 20 Hz to
20,000 Hz is called the audible frequency range.
The sounds we hear comprise of various frequencies.
The entire audible frequency range
can be divided into 8 or 24 frequency bands known
as octave bands or 1/3 octave bands respectively for analysis.
A particular sound or noise can be seen to be
having different strengths or sound pressure levels
in the frequency bands, as illustrated by the
following diagram. Please click on the demo button
to view how sounds can be divided into 8 octave
bands and 24 1/3 octave bands.

One
single sound pressure level is often used to describe
a sound. This can be done by adding
the contribution from all octave bands or
1/3 octave bands together to yield one single
sound pressure level.

The response of the ear to sound is dependent
on the frequency of the sound. The human ear
has peak response around 2,500 to 3,000 Hz
and has a relatively low response at low frequencies.
Hence, the single sound pressure level obtained
by simply adding the contribution from
all octave bands or 1/3 octave bands together
will not correlate well with the non-linear frequency
response of the human ear.

This has led to the concept of weighting
scales. The following diagram shows the "A-weighting"
scale:

In the "A-weighting"
scale, the sound pressure levels for the lower
frequency bands and high frequency bands are
reduced by certain amounts before they are
being combined together to give one single
sound pressure level value. This value is
designated as dB(A). The dB(A) is often
used as it reflects more accurately the frequency
response of the human ear. Weighting networks
are often incorporated in measuring equipments
to give readings in dB(A).