Decibel (dB) Computations

At Cat-Ears / AirStreamz, we are committed to leading industry efforts to bring greater transparency to measuring and reporting wind noise reduction (WNR) effectiveness. This page briefly summarizes the basic quantities of sound and the related decibel / decibel attenuation calculations. Further down the page, we also provide a brief introduction to psychoacoustics and perceived noise reduction. 

By now, you have probably read our basic 'caveat' regarding wind noise:

"Wind noise is a complex phenomenon spanning aerodynamics, acoustics, and the physiology of human hearing.  The amount of wind noise experienced depends on factors like: 1) speed, 2) riding position, 3) wind direction / turbulence level, 4) helmet / eye-wear, 5) hearing impairment / age, and so on."

 

Again, we want to emphasize that determining the 'loudness' of wind noise is problematic because it belongs to psycho-acoustics and this 'personal' feeling is not entirely definable. Loudness as a psychological correlate of physical strength (amplitude) is also affected by parameters other than sound pressure, including frequency, bandwidth, spectral composition, time structure, and the duration of exposure to the (wind) noise. Measured wind noise will not create the same loudness perception by all individuals. 

With that said, let's continue...

Sound and Noise

Sound is something that surrounds us each and every day. The most important thing about sound is that we use it for communication. Communicating can mean many things, it could be a truck driver just listen to the sound from the engine and the engine will communicate to him when it is time to change gear. You can also take pleasure in sound, for example listen to music or take a walk in the forest and listen to some sound there.

 

But what is noise? Every time sound is unwanted, it is called noise. Noise can be harmful and it may damage the hearing. It may also not be harmful, but maybe just annoying. Typically when the neighbour is playing some music it is very annoying, but not when you play music yourself. Noise does not have to be loud to be annoying.

Basic Quantities of Sound

The three different quantities describing sound are sound pressure, sound intensity and sound power. The measurement units used in sound pressure, sound power, and sound intensity are different. Often the measurement unit is omitted during discussions, and only the term “decibels” is used.  This can cause confusion to arise.

Sound pressure is a scalar describing the pressure fluctuation at a given position and is measured in Pascal (Pa). Sound pressure is typically measured at the receiver's position for evaluation of the harmfulness and the annoyance of a noise source.

Sound waves are characterized by compression and expansion of the medium as sound energy (related to acoustic intensity) moves through it. This represents the pressure component of sound. At the same time, there is also back and forth motion of the particles making up the medium (particle motion). The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This energy-amplitude relationship is sometimes expressed in the following manner E  A^2.

Sound pressure, like other kinds of pressure, is commonly measured in units of Pascals (Pa). The quietest sound that most people can hear has a sound pressure of 2 x 10-5 Pa, so this pressure is called the threshold of human hearing.. The level is dependent on the location and distance the sound is observed relative to a sound source. Because your ears are sensitive to a very wide range of sound pressure, it makes sense to use a logarithmic scale to measure the loudness of a sound. Sound pressure level uses a logarithmic scale to represent the sound pressure of a sound relative to a reference pressure. The reference sound pressure is typically the threshold of human hearing: remember that it's 2 x 10-5 Pa.

Sound intensity is a vector quantity that describes the amount and the direction of flow of acoustic energy at a given position. The unit for sound intensity is Watt per square meter (W/m²). Measurement of sound intensity typically needs a special probe consisting of two microphones and a sound intensity analyzer. Sound intensity describes the path of sound and is used for noise source location and rating of noise sources.

Sound Intensity (also known as acoustic intensity) is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2). One application is the noise measurement of sound intensity in the air at a listener's location as a sound energy quantity. Sound intensity is not the same physical quantity as sound pressure

 

Sound power (total sound energy radiated by a source) can only be calculated or determined either based upon sound intensity measurement or based upon sound pressure measurement. The main use of sound power is for noise rating of machines. For comparison of how noisy various machines are, the only way to compare them is to determine the sound power. The unit for sound power measurement is Watts (W).

Power / Source

Intensity / Path

Pressure / Receiver

The Decibel

The Bel (B) was originally developed during the 1920's and used by the telephone industry to quantify power loss in telegraph and telephone signals when sent through long cables.  It is named in honor of Alexander Graham Bell, a pioneer in the field of telecommunications.  One Bel represented a 10-fold gain or loss of power. This turned out to be to be too much change for most measurements and calculations, so the decibel (dB), or 1/10 of a Bel, became the widely used measure of signal change. The metric prefix deci- or d- represents 1/10th or multiplication by 0.1.

Widely used in acoustics, the decibel is nothing more than a logarithmic ratio between two numbers; a measured value and a reference value.  The decibel is only used to compress a wide range of absolute values into a manageable range. It is not an absolute unit. Without a reference level, it means nothing. The ratio may be related to sound power, sound intensity, and sound pressure, etc.

Uses of Decibels

 

Sound intensity or sound pressure level (SPL) is specified in dB. In this case, the reference level of 0 dB corresponds to a pressure of 0.0002 microbars which is the standard threshold for being able to hear a sound. As the sounds get louder, the value of SPL in dB also increases, indicating an increase with respect to the reference level. SPL in the average home is about 50 dB above the 0 dB threshold that serves as the SPL reference. When a vacuum cleaner one meter away is on, SPL increases to 70 dB. A chainsaw one meter away produces a SPL of 110 dB and the threshold of discomfort from sound intensity is 120 dB. Since each 10 dB (or 1 Bel) represents a factor of ten difference, 120 dB (12 Bels) represents a pressure 1012 times greater than the reference threshold level – a change of a million-million! Our ears respond logarithmically to changes in sound level, which makes the “decibel” a very useful tool of comparison

How to Calculate Decibels

While Sound Power Levels and Sound Pressure Levels are expressed in decibels, they have two different equations (as shown below). Equation 1 is for POWER quantities and Equation 2 is for field AMPLITUDE quantities. When expressing a power ratio, the number of decibels is ten times its logarithm to base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing field (root-power) quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The extra factor of two is due to the logarithm of the quadratic relationship between power and amplitude.

Equation 1 (Power):

Equation 2 (Amplitude):

Energy - Amplitude Relationship

The energy transported by a wave is proportional to the to the square of the amplitude of the wave. The energy - amplitude relationship is sometimes expressed in the following manner:

A^2

 

This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. The tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported.

The sound intensity is proportional to the amplitude (sound pressure) squared; I ~ p², so amplitude (sound pressure) is proportional to the square root of sound intensity; p ~ √ I.

  

Sound Perception - Psychoacoustics

When listening, forget the sound intensity as energy quantity. The perceived sound consists of periodic pressure fluctuations around a stationary mean (equal atmospheric pressure).

 

While the intensity of a sound is a very objective quantity that can be measured with sensitive instrumentation, the loudness of a sound is more of a subjective response that will vary with a number of factors. The same sound will not be perceived to have the same loudness to all individuals. Age is one factor that affects the human ear's response to a sound. Quite obviously, your grandparents do not hear like they used to. The same intensity sound would not be perceived to have the same loudness to them as it would to you. Furthermore, two sounds with the same intensity but different frequencies will not be perceived to have the same loudness. Because of the human ear's tendency to amplify sounds having frequencies in the range from 1000 Hz to 5000 Hz, sounds with these intensities seem louder to the human ear. Despite the distinction between intensity and loudness, it is safe to state that the more intense sounds will be perceived to be the loudest sounds.

Psychoacoustics is the scientific study of sound perception and audiology – how humans perceive various sounds. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound (including noise, speech and music). It can be further categorized as a branch of psychophysics. Psychoacoustics received its name from a field within psychology—i.e., recognition science—which deals with all kinds of human perceptions. It is an interdisciplinary field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science. - Ballou, G (2008). Handbook for Sound Engineers (Fourth ed.). Burlington: Focal Press. p. 43.

Equal Loudness Curves

An equal-loudness contour is a measure of sound pressure (dB SPL), over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours. By definition, two sine waves of differing frequencies are said to have equal-loudness level measured in phons if they are perceived as equally loud by the average young person without significant hearing impairment.

Equal-loudness contours are often referred to as "Fletcher-Munson" curves, after the earliest researchers, but those studies have been superseded and incorporated into newer standards. The definitive curves are those defined in the international standard ISO 226:2003, which are based on a review of modern determinations made in various countries.

The Fletcher–Munson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by Harvey Fletcher and Wilden A. Munson, and reported in a 1933 paper entitled "Loudness, its definition, measurement and calculation" in the Journal of the Acoustical Society of America.[1]

Relevance to sound level measurement and noise measurement...

The A-weighting curve—in widespread use for noise measurement—is said to have been based on the 40-phon Fletcher–Munson curve. However, research in the 1960s demonstrated that determinations of equal-loudness made using pure tones are not directly relevant to our perception of noise.[6] This is because the cochlea in our inner ear analyzes sounds in terms of spectral content, each "hair-cell" responding to a narrow band of frequencies known as a critical band. The high-frequency bands are wider in absolute terms than the low frequency bands, and therefore "collect" proportionately more power from a noise source. However, when more than one critical band is stimulated, the signals to the brain add the various bands to produce the impressions of loudness. For these reasons Equal-loudness curves derived using noise bands show an upwards tilt above 1 kHz and a downward tilt below 1 kHz when compared to the curves derived using pure tones.

Various weighting curves were derived in the 1960s, in particular as part of the DIN 4550 standard for audio quality measurement, which differed from the A-weighting curve, showing more of a peak around 6 kHz. These gave a more meaningful subjective measure of noise on audio equipment, especially on the newly invented compact cassette tape recorders with Dolby noise reduction, which were characterised by a noise spectrum dominated by the higher frequencies.

Age Related Hearing Loss / Presbycusis and Perception of Wind Noise

Age-related hearing loss (also known as presbycusis) is a decrease in hearing ability that happens with age. In most cases, the hearing loss affects both ears. It can begin as early as a person's thirties or forties and worsens gradually over time. Age related hearing loss can impact the perception of wind noise and possible annoyance.

Age-related hearing loss first affects the ability to hear high-frequency sounds, such as speech. Affected people find it increasingly difficult to understand what others are saying, particularly when there is background noise (such as at a party). However, because the hearing loss is gradual, many people do not realize they cannot hear as well as they used to. They may turn up the television volume or start speaking louder without being aware of it.

As the hearing loss worsens, it affects more frequencies of sound, making it difficult to hear more than just speech. Determining where a sound is coming from (localization) and identifying its source become more challenging. Some affected individuals also experience a ringing sensation in the ears (tinnitus) or dizziness and problems with balance (presbystasis).

Age-related hearing loss often impacts a person's quality of life. Because affected individuals have trouble understanding speech, the condition affects their ability to communicate. It can contribute to social isolation, depression, and loss of self-esteem. Age-related hearing loss also causes safety issues if individuals become unable to hear smoke alarms, car horns, and other sounds that alert people to dangerous situations.

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