Basic Acoustic Concepts

Knowledge of duct system acoustics is an essential first step.

Sound Power and Sound Pressure

While sounding similar, they are different. Sound power is the amount of acoustical power generated by a sound source in all directions. It is expressed in watts and cannot be directly measured but can be calculated based on sound pressure measurements. Sound power level (abbreviated as PWL or L_w) is a logarithmic measurement of the sound power.

Sound pressure is the fluctuation of the ambient pressure generated by the vibration of a surface that creates a sound wave. It is measurable and expressed in the sound pressure unit pa, or pascal. Sound pressure varies according to the magnitude of the sound source, the location of where the sound is measured, the density of the medium the sound travels through and the directional path the sound travels. The reason why the sound of an electric drill operating in different locations varies is because the sound pressure varies, despite the fact that the sound from the drill is constant.

The range of sound power is huge: a faint noise at the lower level of human audibility is 1x (10)^-12 (0.000000000001) watts, while the sound power of a space shuttle launch is 1 x (10)⁸ (100,000,000) watts. Normal speech is 1 x (10)^-5 (.00001) watts. A soft whisper is 1 x (10^-9) (0.000000001) watts.

Similarly, sound pressure can range from 2 x (10)^-5 (0.00002) pascal to 1 x (10) (100,000)⁵ pascal. Normal speech at 3 feet is 2 x (10)^-2 (0.02) pascal. For convenience and the fact that we cannot hear variations in sound unless there is a large difference in sound pressure, a logarithmic definition of sound power and sound pressure is used. To accommodate such a large span in values, a decibel (dB) is defined as each successive whole number being 10 times larger than the previous number based on a reference point of 20µPascals (20 x 10^-6 pascal). This reference is considered the low threshold of human hearing. Sound pressures are directly measured by a pressure transducer or microphone, which converts pressure to sound pressure levels. Sound Pressure Level (abbreviated as SPL or L_p) is a logarithmic measurement of the sound pressure.

Sound Pressure Level is defined by the equation L_p = 20 log₁₀ (p/p_ref) which results in a dB value with (p_ref=20µPascals). Sound Power Level is defined by the equation L_w = 10 log₁₀ (p/p_ref) which results in a dB value with (p_ref=10^-12 watts).

Note that sound pressure levels are a measurement of pressure where sound power is a measurement of energy.

The unit for both sound power level and sound pressure level is the decibel (dB), which expresses our subjective reaction to noise, or how we perceive sound. Because sound levels are expressed in logarithmic terms, a small change in decibel level is significant in how we hear and perceive that sound.

Calculating sound pressure levels is critical to acoustical analysis because that relates to what sound people will hear.

Since sound power (energy measurement of the sound source) and sound pressure (pressure measurement of the sound we hear) are different, their values in decibels are also different. See Table of Typical Sound Pressure Levels (L_p).

Table 2. Typical Sound Pressure Levels (Lp)

Table courtesy of Kinetics Noise Control, Inc.

Important Points to Remember

• Never specify acoustic treatment without first analyzing both the supply and return air critical duct system paths. • Doing so will result in an improperly designed system that introduces unnecessary costs to the owner. • Avoid over-designing acoustic treatment by considering natural attenuation. • Often natural attenuation is sufficient to reduce noise levels to acceptable limits. * A proper acoustic design goal is to achieve a comfortable acoustical environment not to achieve the lowest possible sound level in a critical space. * Do not over-attenuate high frequencies. A rumble noise problem will be created. • Do not over-attenuate low frequencies. A hissing noise problem will be created. * Some background noise levels can be helpful for speech privacy and masking other noise sources. Identify the use of areas to determine appropriate acceptable noise levels.

 

Combining Sound Levels

Because sound levels are logarithmic, and based on different reference points sound power and sound pressure cannot be directly combined.

A doubling or halving of a sound pressure level will not be perceived as a doubling or halving the level of noise we hear. Rather, since the values are logarithmic it only takes a small change in a sound pressure level to perceive a large change in sound subjective perceptions:

• A change of ± 3 dB is not detectable
• Most people notice a change ± 5 dB
• An increase +10 dB is perceived as a doubling of sound
• A decrease of -10 dB is perceived as a halving of noise