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# Sound basics

What is sound?

Sound may be defined as any pressure variation (in air, water or any other medium) that the human ear can detect.

Knowing the speed and frequency of a sound, we can calculate the wavelength - that is, the distance from one wave top or pressure peak to the next. • Wavelength (Lamda) = Speed of sound / Frequency

From this equation we can work out the wavelength at different frequencies. For example at 20 Hz one wavelength is just over 17 meters, while at 20 kHz, it is only 1,7cm. Thus, we see high frequency sounds have short wavelengths and low frequency sounds have long wavelengths.

A sound which has only one frequency is known as a pure tone. In practice pure tones are seldom encountered and most sounds are made up of different frequencies. Even a single note on a piano has a complex waveform. Most industrial noise consists of a wide mixture of frequencies known as broad band noise. If the noise has frequencies evenly distributed throughout the audible range it is known as white noise and it sounds rather like rushing water.

Sound basic parameters Under free-field conditions

When sound is produced by a sound source with a sound power, P, a transfer of energy from the source to the adjacent air molecules takes place.

This energy is transferred to outlying molecules. Thus the energy spreads away from the source rather like ripples on a pond. The rate at which this energy flows in a particular direction through a particular area is called the sound intensity, I. The energy passing a particular point in the area around the source will give rise to a sound pressure, p, at that point.

r is the density of air, c is the speed of sound.

Note that sound intensity is a vector quantity - it has magnitude as well as direction.

Sound intensity and sound pressure can be measured directly by suitable instrumentation. Sound power can be calculated from measured values of sound pressure or sound intensity levels and a knowledge of the area over which the measurements were made. The main use of sound power is for the noise rating of machines etc. and sound intensity is mainly used for location and rating of noise sources. When it comes to evaluation of the harmfulness and annoyance of noise sources, sound pressure is the important parameter.

Sound pressure

When a sound source such as a tuning fork vibrates it sets up pressure variations in the surrounding air. The emission of the pressure variations can be compared to the ripples in a pond coused by a stone thrown in the water.

The ripples spread out from the point where the stone entered. However the water itself does not move away from the center. The water stays where it is, moving up and down to produce the circular ripples on the surface. Sound is like this. The stone is the source, the pond is the air, and the ripples are the resulting sound wave.

dB - decibel

The advantage of using dB's is clearly seen when a dB scale is drawn on the illustration shown earlier. The linear scale with its large and unwieldy numbers is converted into a much more manageable scale from 0 dB at the threshold of hearing (20 mPa) to 130 dB at the threshold of pain.

Lp = 20 log (p/p0) dB re 20 mPa

(p0 = 20 mPa = 20 × 10-6 Pa)

The sound pressure level, Lp, in dB's is defined as 20 log p/p0 , where p is the measured value in Pa, and p0 is a standardised reference level of 20 mPa - the threshold of hearing. Note here that the word level is added to sound pressure to indicate that the quantity has a certain level above the reference level, and the symbol for sound pressure level is Lp. The illustration shows two examples of how to use the formula for calculation of dB levels. Besides being examples of calculation, these two levels are interesting because they are the levels used for sound level meter calibration

Sound fields

The source we looked at earlier is called a point source and for such a source it was mentioned that the sound pressure drops to half it's value when the distance to the source is doubled. This correspond to a drop in sound pressure of 6 dB.

Another type of source is the line source, which could be a pipe carrying a turbulent fluid, or a road with a high traffic flow. The sound pressure from a line source only drops by approximately 3 dB for a doubling of distance from the source, because the sound spreads out from the source as a wavefront in a direction perpendicular to the line source.

The most rarely found type of sound source when dealing with normal noise measurements is the plane source. A plane source will in principle consist of a piston from which energy is radiated into a tube setting up a plane wave in the tube. Assuming no loss of energy through the walls of the tube, the intensity, i.e. the acoustic energy flowing through the tube, is independent of the distance from the source. Since the intensity is the same everywhere in the tube, the sound pressure level will not drop with an increase in distance from the piston.

In practice, the majority of sound measurements are made in rooms that are neither anechoic nor reverberant - but somewhere in between. This makes it difficult to find the correct measuring positions where the noise emission from a given source must be measured.

It is normal practice to divide the area around a noise source e.g. a machine into four different fields:

• Near field
• Far field
• Free field
• Reverberant field

The near field is the area very close to the machine where the sound pressure level may vary significantly with a small change in position. The area extends to a distance less than the wavelength of the lowest frequency emitted from the machine, or at less than twice the greatest dimension of the machine, whichever distance is the greater. Sound pressure measurements in this region should be avoided.

The far field is divided into the free field and the reverberant field.

In the free field the sound behaves as if in open air without reflecting surfaces to interfere with its propagation. This means, that in this region the sound level drops 6 dB for a doubling in distance from the source.

In the reverberant field, reflections from walls and other objects may be just as strong as the direct sound from the machine.