Lecture 1: Introduction to Sound

Blog One: Sound

Welcome to my blog on Image, Audio and Video Processing. This blog is completed as coursework for my second year university module on the subject, which I am undertaking at the University of the West of Scotland. In this series of blogs I intend to cover various aspects of the subject, starting with this week's blog on Sound.

Sound is transmitted as a wave through a type of medium - normally air, water or metal.  There are two main categories of waves which I will go into detail about- transverse waves and longitudinal waves. Waves will be categorised accordingly depending on the direction of the displacement against the direction of the wave.

Sound Waves- Types:

The best example of transverse waves is a disturbance in water, creating ripples. In a transverse wave the vibrations of the water molecules are at right angles to the motion, moving out from the disturbance.

Longitudinal waves occur if the vibration is parallel to the direction of the motion. The sound wave moves out from the area of disturbance and the individual air molecules move parallel in conjunction with the direction of the wave. The molecules pass energy to the molecules beside them, however as the energy is passed, the molecules remain mainly in the same position.

Compression of a sound wave results in and increase in density, which can be useful as increased density can potentially mean the storage requirements and transmission bandwidth required can significantly reduce. The opposite of this is rarefaction, where density is decreased, the process of this can easily be represented graphically by using a spring as an example. See below to see the difference in wavelength as a direct result of compression or rarefaction.

Sound Calculations

There are three main components in calculations relating to sound, velocity, wavelength and frequency.

Velocity is essentially the speed of sound, although the terminology is slightly different as speed only describes the pace that an object is moving at, whereas velocity also specifies the direction of the movement. Velocity differs for each of the previously mentioned mediums. In air, velocity is roughly 333 metres per second, in steel it travels just under 5000 metres per second and in water it is 1500 metres per second.

Wavelength is the distance between two successive periods of a wave. To simplify this, sound is a succession of waves, all which have the same shape and wavelength is the distance taken for an individual wave to be completed.

Frequency is the number of vibrations per second, to simplify this, it is the number of cycles (individual waves) that are completed each second. Measured in Hertz (Hz) or KiloHertz (KHz).

In layman's terms you could say that you were calculating Speed (Velocity), Distance (Wavelength) and Time (Frequency), but it is more complex than that!

If you have two of these elements, you can work out the third, as shown in the diagram below:

Velocity equals frequency multiplied by wavelength.

Frequency equals velocity divided by wavelength.

Wavelength equals velocity divided by frequency.

An example of a calculation is as follows:

Work out the wavelength of a 1KHz tone going through water.

Velocity in water = 1500 metres per second

Wavelength = Velocity / Frequency

= 1500 / 1000

= 1.5 metres

Sound Particulars

In sound, a standing wave, also known as a stationary wave is a wave which remains in a constant position. This constant position is achieved either because the wave and the medium are travelling in separate directions or it can occur when two waves going in opposing directions interfere with each other.

In a wave, the node is the minimum and can be found at either side, the anti-node is the maximum which occurs in the middle. A standing wave can be supported in a room with nodes situated at opposing walls.

An example of the difference between the two could be described as a standing wave with moving medium could occur due in fast-flowing river rapids or tidal currents, whereas a standing wave which consists of two interfering waves would be likely to occur in open ocean waves.

A sound wave produces a basic tone, which is known as the fundamental tone. A harmonic is an integer multiple of the fundamental tone. For example, if a sound consisted of components at 500hz and 2KHz, the 2KHz would contain a fourth fundamental of the 500hz component.

In simplistic terms, the amplitude is the distance between zero and the highest point of the wave. This is calculated in one of three waves - the energy invovled, the distance travel by the air molecules, or the pressure difference in the compression and rarefaction. Although it can be expressed and understood as the distance between zero and the highest point of the wave, by definition it is the vertical distance between the extrema of the curve and the equilibrim value. 

Sound Measurement

The best method to represent sound intensity (power) level is through decibels, as they can represent a large amount of values. These are defined through a logarithm of the following formula:

This formula demonstrates that multiplying sound intensity level by ten results in an additional 10 decibels of sound. If there was a three times increase in the standard power the equation would be 10log10 (3*P/P).

In order to make this more practical and easier to relate to, below I have included a diagram which on the left hand side states which sounds occur at certain levels of decibels and on the right hand side it depicts how tolerable the human ear is to those sounds. It would appear a live rock band would be the loudest common sound (measured in decibels) that a human is able to tolerate, occuring at 130 DB. Between 150 - 160 Decibels is when sound no longer is tolerable by a human, presenting pain and and a great burden on their ears.


The Inverse Square Law states that a physical quantity or intensity is inversely proportional to the distance from its source (1/R squared). Below is an example of measuring the difference between the sound intensity of two separate distances.

• If the distance was two metres, the sound intensity in the air would be 1/2 squared, which is 1/4
• If the distance was four metres, the sound intensity in the air would be 1/4 squared, which is 1/16
• So comparing the two, sound at two metres from its origin is four times less intense than sound four times from its origin

An echo is defined as the perceived reflection of sound from a surface. This arrives at the listener some time after the initial and direct sound. Echoes can occur from walls, through tunnels and through wells for example. The time delay can be worked out as the extra distance divided by the speed of sound. Echoes first appeared in the music industry in the 1950s and have evolved significantly, with desired echo effects in music today often being achieved by electronic or digital circuitry.

Reverberation is the process which allows copious echoes to build up and transmit before decaying upon the sound being absorbed by the medium creating the echo, i.e. walls or air. Reverberation can occur as a single reflection or as multiple reflections.

Sound graphs can depict time history, showing amplitude against time, and spectrum, showing frequency against time.