Friday, July 31, 2009

Sound and its measurement


Origin of sound
Sound is a variation in the pressure of the air of a type which has an effect on our ears and brain. These pressure variations transfer energy from a source of vibration that can be naturally-occurring, such as by the wind or produced by humans such as by speech. Sound in the air can be caused by a variety of vibrations, such as the following.

Moving objects: examples include loudspeakers, guitar strings, vibrating walls and human vocal chords.
Moving air: examples include horns, organ pipes, mechanical fans and jet engines.
A vibrating object compresses adjacent particles of air as it moves in one direction and leaves the particles of air ‘spread out’ as it moves in the other direction. The displaced particles pass on their extra energy and a pattern of compressions and rarefactions travels out from the source, while the individual particles return to their original positions.

In addition to its link with human hearing the term sound is also used for other movement in air governed by similar physical principles. Disturbances in the air with frequencies of vibration which are too low (infrasound) or too high (ultrasound) to be heard by human hearing are also regarded as sound. Other sound terms in common usage include: underwater sound, sound in solids, or structure-borne sound.

Infrasound: frequency too low for human hearing
Ultrasound: frequency too high for human hearing

Wave motion
The mechanical vibrations of sound move forward using wave motion. This means that, although the individual particles of material such as air molecules return to their original position, the sound energy obviously travels forward. The front of the wave spreads out equally in all directions unless it is affected by an object or by another material in its path. The sound waves can travel through solids, liquids and gases, but not through a vacuum.

It is difficult to depict a longitudinal wave in a diagram so it is often convenient to represent a sound waves as a plot against time of the vibrations. The vibrations can be throught of as the movements of the souce of sound, such as a vibrating loudspeaker, or as the movements of a particle of air. For a pure sound of one frequency, as shown, the plot takes the smooth and regular form of a sine wave.

For diagram visit the source

Sound waves are like any other wave motion and therefore can be specified in terms of wavelength, frequency and velocity.

Wavelength (l) is the distance between any two repeating points on a wave. The unit is the metre (m)

Frequency (f) is the number of cycles of vibration per second. The unit is the hertz (Hz)

Velocity (v) is the distance moved per second in a fixed direction. The unit is metres per second (m/s)

For every vibration of the sound source the wave moves forward by one wavelength. The length of one wavelength multiplied by the number of vibrations per second therefore gives the total length the wave motion moves in 1 second. This total length per second is also the velocity. This relationship between velocity, frequency and wavelength is true for all wave motions and can be written as the formula.

n =f ´ l

where v = velocity in m/s

f = frequency in Hz

l = wavelength in m

The velocity of sound, for any particular material, stays constant. Therefore any increase in freqency, for example, is matched by a decrease in wavelength.

Velocity of sound
A sound wave travels away from its source with a speed of 344 m/s (770 miles per hour) when measured in dry air at 20 °C (68 °F) . This is a respectable speed within a room but slow enough over the ground for us to notice the delay between seeing a source of sound, such as a distant firework, and later hearing the explosion.

The velocity of sound is independent of the rate at which the sound vibrations occur, which means that the frequency of a sound does not affect its speed. The velocity is also unaffected by variations in atmospheric pressure such as those caused by the weather.

But the velocity of sound is affected by the properties of the material through which it is travelling, and the table gives an indication of the velocities of sound in different materials.

The velocity of sound in gases decreases with increasing density as, when the molecules are heavier, then they move less readily. Moist air contains a greater number of light molecules and therefore sound travels slightly faster in moist humid air.

Sound travels faster in liquids and solids than it does in air because of the effect of density and elasticity of those materials. The particles of such materials respond to vibrations more quickly and so convey the pressure vibrations at a faster rate. For example, steel is very elastic and sound travels through steel about 14 times faster than it does through air.

Table of Velocity of sound
Typical velocity (m/s)

Air (0°C)

Air (20°C)

Water (25°C)





Frequency of sound
If an object that produces sound waves vibrates 100 times a second, for example, then the frequency of that sound wave will be 100 Hz. The human ear hears this as sound of a certain pitch.

Pitch is the frequency of a sound as perceived by human hearing.
Low-pitched notes are caused by low-frequency sound waves and high-pitched notes are caused by high-frequency waves. The pitch of a note determines its position in the musical scale. The frequency range to which the human ear responds is approximately 20 to 20 000 Hz and frequencies of some typical sounds are shown in the figure.

‘bass’ = low frequency
‘treble’ = high frequency
Most sounds contain a combination of many different frequencies and it is usually convenient to measure and analyse them in ranges of frequencies, such as the octave.

An Octave Band is the range of frequencies between any one frequency and double that frequency.
Quality of sound
A pure tone is sound of only one frequency, such as that given by a tuning fork or electronic signal generator. Most sounds heard in everyday life are a mixture of more than one frequency, although a lowest fundamental frequency predominates when a particular ‘note’ is recognisable. This fundamental frequency is accompanied by overtones or harmonics.

Overtones and Harmonics are frequencies equal to whole-number multiples of the fundamental frequency.
For example, the initial overtones of the note with a fundamental of 440 Hertz are as follows:

440 Hz = fundamental or 1st harmonic

880 Hz = 1st overtone or 2nd harmonic

1320 Hz = 2nd overtone or 3rd harmonic etc.

Different voices and instruments are recognised as having a different quality when making the same note. This individual timbre results because different instruments produce different mixtures of overtones that accompany the fundamental. The frequencies of these overtones may well rise to 10 000 Hz or more and their presence is often an important factor in the overall effect of a sound. A telephone, for example, transmits few frequencies above 3000 Hz and the exclusion of the higher overtones noticeably affects reproduction of the voice and of music.

Cancellation of sound
The nature of a sound wave, such as shown in the earlier figure, means that the vibration of the wave has alternate changes in amplitude called phases. If a wave vibration in one direction meets an equal and opposite vibration, then they will cancel. The effect of this phase inversion in sound waves is to produce little or no sound and gives the possibility of ‘cancelling’ noise. This is the principle of Active Noise Reduction (ANR) used in some headsets and aircraft for example.

Every object has a natural frequency which is the characteristic frequency at which it tends to vibrate when disturbed. For example, the sound of a metal bar dropped on the floor can be distinguished from a block of wood dropped in the same way. The natural frequency depends upon factors such as the shape, density and stiffness of the object.

Resonance occurs when the natural frequency of an object coincides with the frequency of any vibrations applied to the object. The result of resonance is extra large vibrations at this frequency.

Resonance may occur in many mechanical systems. For instance, it can cause loose parts of a car to rattle at certain speeds when they resonate with the engine vibrations. The swaying of a suspension bridge can resonate with footsteps from walkers. The shattering of a drinking glass has been attributed to resonance of the object with a singer’s top note! Less dramatic, but of practical application in buildings, is that resonance affects the transmission and absorption of sound within partitions and cavities.


The uneven sensitivities of the human hearing system lead us to measuring sound by a logarithmic decibel scale which is progressively 'squashed' rather than being a uniform scale. It happens that this is also the way that our hearing perceives sound energy or strength. So the simple energy or pressure measurements of sound are converted to sound level values in decibels (dB) which are easier numbers for humans to understand and relate to. Extra-terrestrial beings, or even your cat, might well prefer the unconverted values!

Sound levels in decibels start with a zero at the threshold of hearing which is the weakest sound that the average human ear can detect Typical effects of sound levels and changes in sound levels are shown in the illustrations. Remember that there is distinct difference between a change in energy and a change in our idea of loudness.

A change in sound level of + or - 10 dB is a useful figure to remember as it makes difference of approximately twice as loud, or half as loud. We have to say 'approximately' as the experience also depends on individual hearing, on the background noise and on the exact frequencies involved. An increase in sound level of 20 dB (10 dB then another 10 dB) will seem four times

For example, there may be a proposal to increase the average sound level of your environment from 60 dB to 70 dB. This seems a relatively small change, after all the scale runs from 0 to 140 but it will make the environment twice as noisy.

The same idea applies to reducing noise. If the manufacturers of a certain machine can reduce the sound level from 90 dB to 80 dB then the machine will sound approximately half as loud as before.

For Table of Decibel scale visit the source

Sound Meters are also explained in the source article in knol.

Visit the source for diagrams and updated versions.


Sound and its measurement, Randall McMullan

The article is in Creative Commons Attribution 3.0 License on 31.7.2009

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