The Engineer's Guide to Sound Attenuation

The risk of physical damage to human beings, domestic animals, and wildlife from noise is well documented. Temporary or permanent hearing loss may result from noise exposure of excessive intensity and duration.

Hazardous noise risks infographic

While the risks exist everywhere, the workplace is the primary environment for the potentially hazardous effects. It has been estimated that 14 million U.S. workers are exposed to hazardous noise.

The Occupational Safety and Health Act (OSHA) states that every employer is legally responsible for providing a workplace free of hazards such as excessive noise. Fortunately, noise exposure can be controlled, and the technology exists to reduce the dangers.

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Sound is a propagating vibrational disturbance created by an oscillation in pressure, stress, particle displacement, and particle velocity in an elastic medium (solid, liquid, or gas). Sound is most commonly considered an auditory sensation to the human ear, evoked by the disturbance.

Sound waves are usually modeled as a sinusoidal function. The following figure (a sine wave) shows a single frequency at a constant amplitude. The zero line represents atmospheric pressure with positive sound pressure above the line and negative below the line. This variation in pressure causes the eardrum to cycle in and out. The inner ear processes the physical motion into what we hear. If the sound energy is too high, it can damage the ear.

Pressure-distance graph

Pressure-Distance Graph

Compression C: Highest pressure

Rarefaction R: Lowest pressure

Amplitude A: The maximum pressure change from surrounding pressure in either direction

Wavelength λ: The distance between two consecutive C or R or any two points that are in phase.

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business woman covering her earsNoise is any unwanted sound or a meaningless sound of greater than usual volume. It can be defined as a discordant sound resulting from non-periodic vibrations in the air or, more commonly, unwanted sound (noise pollution). The effects of noise may be categorized as follows:

  • Hearing loss
  • Non-auditory health effects
  • Impact on individual behavior
  • Adverse effects on sleep
  • Communication interference
  • Effects on domestic animals and wildlife

Additionally, noise can evoke emotional responses on conscious and subconscious levels. It annoys, angers, frustrates, and creates stresses that result in physiological and psychological problems. Though it is invisible, its effects are clearly evident, and it pervades every facet of life.

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Frequency and Bandwidths

Frequency is defined as the number of cycles per second of an oscillation. On a piano, middle C represents a pure tone at 250 Hz. Human beings have an audible frequency range of about 20 Hz to 20,000 Hz. The frequency range is commonly divided into octave bands, each identified by the center frequency. For more detailed analysis, octave bands can be sub-divided into 1/3 octave bands.

Heavy construction site with drills

The frequency band identifies the sound energy so a noise control device can be effectively designed. The most common bandwidths used are the nine-octave bands from 31.5 Hz to 8k Hz. The sound level in each band can be significantly different from the adjacent band.  Machinery noise is not usually a concern above the 8k Hz band, but it may be in the 16 Hz band for very low-frequency sounds and 16k Hz for very high-frequency sounds.  When designing noise control devices, using octave or one-third octave bands is normally acceptable.

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Frequency Weightings

The human ear is a dynamic filter that shifts its sensitivity to sound, based on the amplitude and frequency of the sound. The ear performs very well at middle frequencies but is relatively insensitive to very low and very high frequencies

Frontal section through the right external, middle, and internal earTo analyze the human response to sound, researchers developed sound equipment to electronically simulate the way sounds are filtered by the ear. Electronic processing is applied to the sound to simulate a biological function (hearing) utilizing weighting curves commonly known as A, B, C, D, and E.

A-weighting tracks the frequency sensitivity of the human ear at low levels. The most commonly used weighting scale, it accurately predicts the damage risk of the ear. Sound level meters set to the A-weighting scale simulate the response of the human ear by filtering out much of the low-frequency noise they measure. Noise measurements made with the A-weighting scale are designated dBA.

B-weighting tracks the frequency sensitivity of the human ear at moderate levels. The B-weighted scale was often used in the past for predicting the performance of loudspeakers but not industrial noise.

C-weighting tracks the frequency sensitivity of the human ear at very high noise levels. The C-weighting scale is flat and, therefore, includes more of the low-frequency range of sounds than the A and B scales.

The C-weighting scale was originally considered to be the best predictor of the ear’s sensitivity to tones at high noise levels. However, the A-weighted sound level was adopted for most environmental conditions, because the ear’s loudness sensitivity for tones is different from the ears’ damage risk for noise.

Even though the low and high frequencies are perceived as being equally loud at high sound levels, the ear filters out much of the low-frequency noise, making it less likely to cause damage. The A-weighting scale in a sound level meter imitates the filtering process of the human ear.

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Sound Pressure Levels

Sound is proliferated as a fluctuation in pressure above and below the ambient atmospheric pressure. The amplitude of these fluctuations is proportional to sound volume or how loud something is perceived to be. The human ear can detect an extremely large range of pressure fluctuations.

In acoustics, there is a logarithmic relationship between sound pressure and sound pressure level, so the decibel (dB) scale is used to describe sound pressure levels. The decibel level is defined as:

  • SPL or Lp = 20 Log (P/Pr)   dB, re: 20 micro-Pascals―where P is the sound pressure and Pr is the reference value (20 micro-Pascals)

A sound meter microphone and electronics process sound pressure measurements and present sound level (the rms amplitude) in decibels.  

So, how sensitive is our hearing and how does a decibel sound level correlate with what we hear?  The following table shows typical sound levels in the home, work, and recreation environments.

Typical Sound Levels in Decibels

Typical Sound Levels in Decibels table

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Sound Power Levels

Sound power is the acoustical power (watts) emitted by the source. It is independent of the environment and is dependent only on the operating conditions of the equipment. Equipment is rated in terms of sound power levels, which permits calculation of expected sound levels.

black electric heater on laminate floor in the roomAn electric room heater is a good analogy to show the distinction between sound power and sound pressure. The heater emits a specific amount of heat energy, measured in watts; a power rating that is independent of the surroundings. However, the temperature measured in the room will also depend on the distance from the heater, heat absorbed by the walls, heat transfer through the walls and windows, and other objects in the room.

Similarly, a sound source has a certain amount of sound energy or power level. The farther away from a device, the lower the sound pressure level, but the sound power level is the same. Sound power is calculated:

  • Lw = 10×log (w / wref)―where w is the acoustic energy radiated by the source.
  • The reference power is 10-12  watts―(w) is the lowest sound people with excellent hearing can discern.
  • Sound power is a measurement of the total sound power emitted by a source in all directions.

Sound level meter with needleThere are several general techniques for determining sound power levels that cannot be measured directly. Sound power levels are calculated from sound pressure or intensity measurements in a controlled environment.

If we have sound power data, we have the absolute acoustical energy, and it is a distinct advantage over just having sound pressure levels or sound level data, which require detailed measurement information. The distance from the device and the area over which the measurement was made must be well defined.

The physical relationship between sound power and sound pressure is defined:

  • LW = Lp + 10 Log (S)   dB re: 1 pico-Watt―where the “S” term describes the area over which sound pressure levels (Lp) were measured. The equation demonstrates the importance of defining the measurement area to arrive at an accurate calculation of sound power level.

Sound power is critical to modeling and calculating sound propagation as follows:

  • Lp = LW – 10 Log (S)   dB re: 20 micro-Pascals (5)―the sound level at the receiver (Lp) is dependent upon “S” (distance from the source) and the sound power level (LW).  By knowing the sound power level, the sound level at any location can be calculated.

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Approach to Noise Control: Source-Path-Receiver

Any noise control problem can be reduced to its fundamental components: a source that creates the noise, a path that conveys the noise, and a receiver that hears the noise. several options are available for diminishing the noise at each component.

address noise quote

The most desirable and effective option is to address the noise at the source. Selection of quiet equipment can minimize or even eliminate many potential noise problems at the outset. Treatment measures along the path are the next best option. These can include silencers, barriers, absorption, lagging, or other options.

The last resort, and least desirable, is noise treatment at the receiver; i.e., hearing protection from loud occupational exposure in the form of ear plugs or other types of ear covers.

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Sound Sources

Big industrial fan in a factoryIt is important to obtain source sound power levels from the equipment supplier. The sound power levels should be derived from tested performance according to an industry-recognized standard that applies to the equipment in question.

For example, fans are commonly tested according to AMCA 300 or 320, Air Handling units per AHRI 260, and terminal units according to ASHRAE 130. Recognized standard testing ensures that the results can be fairly compared and evaluated between manufacturers.

Estimates of power levels should only be used where manufacturer supplied data is not available. Common sound sources in an HVAC system are fans, element generated flow noise, VAV components, and mechanical equipment.

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Once the noise source has been acknowledged, the position in relation to the receiver can be determined and the path by which the noise is transmitted can be identified. Noise typically travels through multiple paths, both airborne and structural. All possible paths must be acknowledged and evaluated correctly. Once one path has been treated, another path may become dominant and any further treatment to the first path will no longer be effective.

The Sound Paths diagram (below) illustrates possible transmission paths for the sound and vibration from the source to the receiver. In this example, the sound source is an air handler that contains both a fan and a compressor; the receiver is the human occupant in the adjacent room.

Path A – Structure-borne path: the air handler vibration passes through the floor.

Path B – Airborne path: the equipment noise radiates directly to the receiver.

Path C – Duct-borne path: the equipment noise radiates through the ductwork walls or passes through the supply/return ductwork into the occupied space.

Engineering Guide Noise Control Illustration

Illustration from Engineering Guide Noise Control, Price Engineers HVAC Handbook

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Acoustical Spectra

When designing noise control equipment, the source frequencies must be identified and, generally, the type of problem will dictate the type of measurements.

The figure below displays two sound pressure level (SPL) measurements (solid lines) and their corresponding A-weighted levels (dash lines) for a typical broadband noise source. Just looking at the data, one would conclude that the major acoustical energy is in the 63 Hz to 100 Hz bands.  

However, A-weighted dash lines on the graph show that the dominating sound level, as heard, is the acoustical energy in the 1,000 Hz and 1,250 Hz bands. The data demonstrates the relative importance of using A-weighted analysis to assess a measurement and identify where noise control measures need to be implemented.

Blow-off Vent Measurements

Blow-off Vent Measurements

One-third Octave band Center Frequency, Hz

Unweighted vs. A-weighted Measurement

The figure above shows the importance of obtaining accurate and adequate field measurements when solving noise problems. Narrowband frequency measurements are important to identify the exact noise frequencies. As shown in the figure above, any noise control treatment would need to focus on the 1,000 Hz and 1,250 Hz bands.   

The data were obtained using a sound analyzer that processes the measurements into frequency-based sound pressure levels (SPLs). Only an A-weighted sound level A sound level meter can perform this type of measurement.

A silencer or noise control device cannot be designed to simply reduce an overall sound level. The device must consider the source frequencies and the human hearing sensitivity represented by the A-weighted data. With accurate and complete data and information, a noise control solution can be designed to effectively reduce noise to an acceptable level or eliminate it completely.