Relationship ofSound Pressure and Sound Po^e^

In acoustics of building mechanical systems, sound energy is often represented as one of two quantities: sound pressure levels or sound power levels. Sound pressure level is the most common form of describing the human response to airborne sound, and measures the changes in pressure with respect to static pressure. This quantity is dependent upon the distance of the receiver to the source and the environment in which it is measured. However, another quantity, sound power level, is independent of distance to the source and the environmental characteristics of the space. Sound power describes the rate at which sound energy is produced by a source and is used to quantify the sound energy relating to mechanical equipment. Using an acoustical predictor that is independent of the environment allows for simple comparison of acoustical characteristics of mechanical equipment.

Although sound power is a common descriptor of acoustical energy, there is no easy way to measure sound power directly. A collection of sound pressure measurements can be used to calculate sound power. Other information is necessary including the directivity of the source, the distance of the measurements, environmental characteristics, and the area that the measurements cover. The actual equation used for converting between sound pressure level and sound power level varies with the situation (Bies & Hansen, 2003).

Sound Propagation in Ducts

There are three issues associated with the sound propagation in ducts that affect in-duct measurementshe characteristics of acoustical energy in ducts, end reflections, and turbulence. The first issue of acoustical characteristics depends on the dimensions of the duct and the frequencies being measured. At lower frequencies with large wavelengths, only plane waves propagate in a duct and a simple relationship can be shown between sound pressure and sound power. At high frequencies with shorter wavelengths, plane modes and higher order modes can exist. This means that sound is propagating not only parallel to the axis of the duct but also in various angles due to reflections off the wall of the duct. These modes cause variations in the sound pressure level at particular locations in a cross-sectional area of the duct. Modes in the duct will vary based on the dimensions of the duct and the frequency of the measurements. These modes can cause interference that results in a change in measured energy.

The second issue when taking in-duct measurements is end reflection factors due to duct termination. An opening at the discharge of a duct can create end reflections that send a sound wave back into the duct against the airflow because of an impedance mismatch. The reflections can cause interference and generate standing waves that further complicate the patterns of sound energy being transmitted through each element of the duct system. Such standing waves in the duct can cause inaccuracies with in-duct measurements of element contributions.

The third issue with in-duct measurements is turbulence caused by the movement of air in the duct. Turbulence can be caused by obstructions to the flow and other changes in pressure. The resulting turbulent eddies have flow that may not be parallel to the axis of the duct. The turbulent fluctuations in pressure can not be differentiated by a microphone measuring the pressure changes associated with acoustical energy. These pressure fluctuations affect random frequencies of measurements taken in such a condition (Liao, 1990).源'自^吹冰],论`文'网]www.chuibin.com

Measuring Sound Energy in Ducts

All three sound propagation issues must be addressed when making in-duct measurements to obtain reliable acoustical data. In existing standards, the three issues are addressed by obtaining the data in a controlled laboratory environment. These

existing standards can serve as a guideline to create a method of in-duct measurement for obtaining the desired sound power measurements at a particular point in a duct.