Sound as wave motion

An airborne sound can be seen as an air pressure variation in the air. It has a wavelength, frequency and intensity. Sound travels from the source to the point of reception in a media. When energy strikes the molecules of the media, it causes the molecules to vibrate back and forth, producing a wave that transmits sound energy. The speed of sound depends on the medium the waves pass through, and is a fundamental property of the material. A solid is an excellent transmitter of sound, liquids do not transmit sound very well and gases are the poorest transmitters of sound. For example, sound travels in air at nearly 340 metres per second, but it can travel through steel at about 5,200 metres per second.

Since a sound wave consists of a repeating pattern of high pressure and low pressure regions moving through a medium, it is sometimes referred to as a pressure wave. Sound waves are often depicted in graphs like those below, where the x-axis is time and the y-axis is pressure or the density of the medium through which the sound is travelling. physical value symbol unit formula frequency f=1/T Hz=1/s f=c/λ wavelength λ m λ=c/f time period or cycle duration T=1/f s T=λ/c wave speed c m/s c=λxf

The human ear is extremely sensitive and only low power intensities are needed for hearing. The human hearing range is in the area between 0 dB (hearing threshold) and 120 dB (pain threshold) in frequencies between 20 – 20000 Hz. Frequencies which fall below the hearing area are known as infrasound and frequencies above 20000 Hz are called ultrasound.

The most important frequency range from the speech distinctness point of view is 300 – 3000 Hz. Noises are not usually pure tones, but include a range of sound energy spread over a wide band of frequencies. The centre frequencies are internationally standardised and the table below shows some of the standard frequency bands.  The human ear responds to sound pressure, which is measured in units of Pa (N/m2). The lowest sound pressure that an average ear can detect is about 0.00002 Pa, and the limit for pain is about 200 Pa. Because of this extensive range in pressure, it is impractical to use a linear scale, so sound pressure levels are generally expressed using a logarithmic scale (denoted as dB). The terms dB and bel (=10 dB) are actually pure mathematical terms and are not dedicated especially to acoustics.

Bel is the logarithm for the relationship between two quantities.

The experience of a sound varies from person to person. A sound hardly recognised by one person can be very irritating to someone else. Individuals can also react differently to the same sound depending on the mood. Generally an increase of 10 dB is perceived as a doubling of the sound level and 1–2 dB is the smallest change that the ear can imagine.

 The experience of sound depends on The sound level The frequency The type of sound, if it is constant or intermittent If it is noise or nice music Decibel arithmetic

As stated previously, the decibel is a logarithmic value that cannot be added or subtracted in the same way as linear values. It is therefore necessary to return to linear units, Pa, in order to perform the arithmetic and then to go back to logarithmic values.

As an example, add the two sound level values:

 Lp1= 40 dB and Lp2=45 dB First, change the units to bels by dividing by 10 and then return to linear values in order to perform the addition: 104.0 + 104.5 =10 000 + 31 622 = 41 622 Then returning to logarithmic values gives: log (41 622) = 4.62 bel So that: Lp.tot = 46.2 dB Alternatively, the figure on the right side may be used to obtain the same result. Mathematically, the addition of two identical sources will increase the level by 3 dB and 10 identical sources by 10 dB. This can also been shown by the following figure. When the sound level is measured the sensitiveness of the ear is considered by using different filters. These filters are marked as dB(A), dB(B) and dB(C). The most often used filter is the A-weighted filter, which imitates the way an ear filters sound. See the figure below (the attenuation curve for the A-filter). Picture: the attenuation curve for the A-filter

Reflection, sound absorption and sound insulation

Sound may be absorbed, transmitted or reflected. When a room boundary, such as a roof, floor or a wall, is hit by a sound wave, some of the sound energy will be reflected, some is absorbed within the material and some is transmitted through it, as illustrated by the figure. The proportion which is reflected, absorbed or transmitted depends on the shape of the material or the construction hit by the sound wave, and the frequency of the sound. Based on this, three acoustical parameters can be defined.

Absorption coefficient, α = (absorbed sound + transmitted sound)/(incident sound)

Reflection coefficient, ζ = (reflected sound)/(incident sound)
Transmission coefficient, τ = (transmitted sound)/(incident sound)