# The Decibel and Sound Pressure – Class Research

The Decibel and Sound Pressure – Class Research

Here is a Google Docs shared, Class Researched (but unverified) document for all you may need to know on Decibels. It was done in minutes with the whole class cutting and pasting info from the web simultaneously via Google Drive and Docs.

Definition:

The decibel (dB) is a
logarithmic unit used to express the ratio between two values of a physical quantity (usually measured in units of
power or
intensity). One of these quantities is often a reference value, and in this case the dB can be used to express the absolute level of the physical quantity. The decibel is also commonly used as a measure of
gain or
attenuation, the ratio of input and output powers of a system, or of individual factors that contribute to such ratios. The number of decibels is ten times the
logarithm to base 10 of the ratio of the two power quantities.[1] A decibel is one tenth of a bel, a seldom-used unit named in honor of
Alexander Graham Bell
.

Maths:

The
sound intensity
I may be expressed in decibels above the standard
threshold of hearing
I0 . The expression is

The
logarithm
involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. Example: If I= 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 104, the power of ten is 4, and the intensity is 40 dB:

The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because about 1 decibel is the
just noticeable difference (JND)
in sound intensity for the normal human ear.

Decibels provide a relative measure of sound intensity. The unit is based on powers of 10 to give a manageable range of numbers to encompass the wide range of the human hearing response, from the standard threshold of hearing at 1000 Hz to the
threshold of pain
at some ten trillion times that intensity.

Another consideration which prompts the use of powers of 10 for sound measurement is the
rule of thumb for
loudness
: it takes about 10 times the intensity to sound twice as loud.

?
Decibel Table ?
SPL ?
Loudness Comparison Chart
?

Table of
Sound Levels
(dB Scale) and the corresponding

Units of
Sound Pressure and
Sound Intensity
(Examples)

 To get a feeling for decibels, look at the table below which gives values for the sound pressure levels of common sounds in our environment. Also shown are the corresponding sound pressures and sound intensities. From these you can see that the decibel scale gives numbers in a much more manageable range. Sound pressure levels are measured without weighting filters.
 The term “loudness” or “volume” is a problem because it belongs to psycho- acoustics and this personal (subjective) feeling is really difficult to “measure”.
 The values are averaged and can differ about ±10 dB. With sound pressure is always meant the root mean square value (RMS) of the sound pressure, without extra announcement. The amplitude of the sound pressure means the peak value. The sound pressure (RMS) is the most important quantity in sound measurement. Our hearing is a sound pressure receptor, or a sound pressure sensor, because the eardrums (tympanic membranes) are moved by the sound pressure as a sound field quantity. That is the important effect of the excess sound pressure. It is not an energy receiver! When listening to music, forget the sound intensity as energy quantity. The perceived sound consists of periodic acoustic pressure vibrations (sound pressure) which are superimposed on the surrounding static air pressure of 101?325 Pascal (mean atmospheric pressure). The sound is the change of sound pressure p, which is measured in pascal. Pa ? 1 N/m2 ? 1 J / m3 ? 1 kg / (m·s2). Usually p is the RMS value.
 Sound sources (noise) Examples with distance Sound pressure Level Lp dB SPL Jet aircraft, 50 m away 140 Threshold of pain 130 Threshold of discomfort 120 Chainsaw, 1 m distance 110 Disco, 1 m from speaker 100 Diesel truck, 10 m away 90 Kerbside of busy road, 5 m 80 Vacuum cleaner, distance 1 m 70 Conversational speech, 1 m 60 Average home 50 Quiet library 40 Quiet bedroom at night 30 Background in TV studio 20 Rustling leaves in the distance 10 Hearing threshold 0
 Sound pressure p N/m² = Pa Sound field quantity Sound intensity I W/m² Sound energy quantity 200 100 63.2 10 20 1 6.3 0.1 2 0.01 0.63 0.001 0.2 0.000?1 0.063 0.000?01 0.02 0.000?001 0.006?3 0.000?000?1 0.002 0.000?000?01 0.000?63 0.000?000?001 0.000?2 0.000?000?000?1 0.000?063 0.000?000?000?01 0.000?02 0.000?000?000?001
 Wrong question: “Jackhammer. How many dBs?” The distance is missing! Notice: A given sound level without given distance is really useless.
 Sound pressure p (RMS) as Sound field quantity: The auditory threshold is used as the reference sound pressure p0 = 20 µPa = 2 × 10?5 Pa. The threshold of hearing corresponds to the sound pressure level Lp = 0 dB at f = 1 kHz. Sound intensity I as Sound energy quantity: The auditory threshold is calculated as the reference sound intensity I0 = 10?12 W/m2. The threshold of hearing corresponds also to the sound intensity level LW = 0 dB at f = 1 kHz. Sound pressure p = ? (I × Z0) Sound intensity I = p2 / Z0 acoustic impedance Z0 = 400 N·s/m3

What does sound level mean?

 Sound engineers and “ear people” think by the short word “sound level” simply of “sound pressure level” as sound field quantity. Acousticians and “noise fighters” mean by the short word “sound level” probably “sound intensity level” as sound energy quantity. Equating sound pressure with sound intensity must cause problems. I ~ p2.
 The sound level depends on the distance between the sound source and the place of measurement, possibly one ear of a listener. The sound pressure level Lp in dB without the given distance r to the sound source is meaningless. Unfortunately this error (unknown distance) is quite often to find. Many users really wrongly believe that a sound source must have a fixed dB value; e.g. jackhammer = 110 dB and jet plane = 130 dB. Distance ??? The threshold of pain, depending on the frequency composition, is to find between 120 dB and 140 dB.
 What is loud? Noise is a sound that disturbs or harms.
 What we condemn as noise depends not only on the noise level. There are social, physical and psychological factors. Besides the type of noise and personal noise sensitivity there are the expectations of a person which is crucial to its assessment of noise. The “desired” noise is not the classification in ‘noisy’ or ‘too loud’. Kurt Tucholsky wrote: “Our own dog does not make noise, it only barks” and “noise is the sound of the others.”
 What is the highest sound pressure possible? How many decibels is the loudest noise?
 Assumption: The maximum sound pressure that cannot be exceeded because the average air pressure is 101325 Pa. This sound pressure level is: L = 20 × log (101?325 / 0.000?02) = 194 dB SPL. Pay attention, RMS value is not peak value. A typical false statement: “No noise levels can exceed 194 dB ever”. Is the end at 194 dB? In addition to this perception threshold is discussed more often a physical limit to 194 dB. Sound is nothing more than a minor disturbance of air pressure and 194 dB is theoretically the same as the disturbance itself. It must be asymmetric. Even louder noise is possible, but heavily distorted. That’s chaos. This high sound pressure will break all measurement microphones and human beings are completely torn when they are close to the center of a nuclear explosion. No hearing protection (ear muffs or ear plugs) can help you there. These madness sound levels will never be measured but only estimated or calculated. Ultrasound between 20 kHz and 1.5 GHz does not belong to our human hearing. Infrasound below about 16 Hz is not audible for the human ear, but we can feel high sound levels.
 The total sound power is emitted by the sound source. Sound power levels are connected to the sound source and are independent of distance. Sound pressure levels vary substantially with distance from the source.
 Sound pressure p in pascals (newtons per square meter) is not the same physical size as intensity J or I in watts per square meter. … and the sound power (acoustic power) does not decrease with distance r from the sound source – neither with 1 / r nor as 1 / r2.
 Sound Field Sizes Sound pressure, sound or particle velocity, particle displacement or displacement amplitude, (voltage, current, electric resistance). Sound Energy Sizes Sound intensity, sound energy density, sound energy, acoustic power, (electrical power).

Direct
conversion
of sound pressure to sound intensity and vice versa.

 Simply enter the value to the left or the right side. The calculator works in both directions of the ? sign.
 Sound field quantity Sound energy quantity Sound pressure p (air) Pa ? Sound intensity I (air) W/m2 Reference sound pressure p0 = 20 ?Pa = 2 × 10?5 Pa Reference intensity I0 = 1 pW/m2 = 10?12 W/m2 Specific acoustic impedance of air Z0 = 400 N·s/m3 Sound pressure p = ? (I × Z0) Intensity I = p2 / Z0
 Sound field quantity Sound energy quantity Sound pressure level Lp (air) dB ? Sound intensity level LI (air) dB Reference sound pressure p0 = 20 ?Pa = 2 × 10?5 Pa Reference intensity I0 = 1 pW/m2 = 10?12 W/m2 The same “sound level” in dB at Specific acoustic impedance of air Z0 = 400 N·s/m3
 While the sound pressure level in the air is matched with the sound intensity level when a reference sound characteristic impedance Z0 = 400 N·s/m³ is chosen, this is not the case with the distance independent sound power level.
 There is no “dBA” value given as threshold of human hearing. These values are not given as dBA, but as dBSPL, that means without any weighting filter.

Comparison of sound pressure level SPL and sound intensity level

 Differentiate between sound pressure p as a “sound field size” and sound intensity I as a “sound energy size”. I ~ p2 for progressive plane waves. When it comes to our ears and the hearing, it is recommended that the inappropriate expression of the sound energy parameters, such as sound power (acoustic power) and sound intensity to leave aside. So we are just listening to the sound pressure as sound field size, or the sound pressure level SPL. The sound pressure level decreases in the free field with 6 dB per distance doubling. Often it is argued the sound pressure would decrease after the 1/r2 law (inverse square law). That’s wrong. The sound pressure in a free field is inversely proportional to the distance from the microphone to the source. p ~ 1/r.

How does the sound decrease with increasing distance?

Relation of sound intensity, sound pressure and
distance law
:

 From this follows
 Note: The often used term “intensity of sound pressure” is not correct. Use “magnitude”, “strength”, “amplitude”, or “level” instead. “Sound intensity” is sound power per unit area, while “pressure” is a measure of force per unit area. Intensity (sound energy size) is not equivalent to pressure (sound field size).
 dB scale for field sizes, like volts and sound pressures ratio
 The sound pressure is the force F in newtons N of a sound on a surface area A in m2 perpendicular to the direction of the sound. The SI-unit for the sound pressure p is N/m2 = Pa. p ~ 1/r.

How to measure sound pressure?

 By the way, sellers always want us to buy a sound pressure level meter with digital display. But much better, however, is an analogue-to-read display – as in this figure.
 Note – Comparing dBSPL and dBA: There is no conversion formula for measured dBA values to sound pressure level dBSPL or vice versa. That is only possible measuring one single frequency. There is no “dBA” curve given as threshold of human hearing. The weighted sound level is neither a physiological nor a physical parameter.
 Pro audio equipment often lists an A-weighted noise spec – not because it correlates well with our hearing – but because it can “hide” nasty hum components that make for bad noise specs. Words to bright minds: Always wonder what a manufacturer is hiding when they use A-weighting. *)

Readings of a pure 1 kHz tone should be identical, whether weighted or not.

How loud is dangerous?

Typical dbA levels

 190 dBA Heavy weapons, 10 m behind the weapon (maximum level) 180 dBA Toy pistol fired close to ear (maximum level) 170 dBA Slap on the ear, fire cracker explodes on shoulder, small arms at a distance of 50 cm (maximum level) 160 dBA Hammer stroke on brass tubing or steel plate at 1 m distance, airbag deployment very close at a distance of 30 cm (maximum level) 150 dBA Hammer stroke in a smithy at 5 m distance (maximum level) 130 dBA Loud hand clapping at 1 m distance (maximum level) 120 dBA Whistle at 1 m distance, test run of a jet at 15 m distance Threshold of pain, above this fast-acting hearing damage in short action is possible 115 dBA Take-off sound of planes at 10 m distance 110 dBA Siren *) at 10 m distance, frequent sound level in discotheques and close to loudspeakers at rock concerts, violin close to the ear of an orchestra musicians (maximum level) 105 dBA Chain saw at 1 m distance, banging car door at 1 m distance (maximum level), racing car at 40 m distance, possible level with music head phones 100 dBA Frequent level with music via head phones, jack hammer at 10 m distance 95 dBA Loud crying, hand circular saw at 1 m distance 90 dBA Angle grinder outside at 1 m distance Over a duration of 40 hours a week hearing damage is possible 85 dBA 2-stroke chain-saw at 10 m distance, loud WC flush at 1 m distance 80 dBA Very loud traffic noise of passing lorries at 7.5 m distance, high traffic on an expressway at 25 m distance 75 dBA Passing car at 7.5 m distance, un-silenced wood shredder at 10 m distance 70 dBA Level close to a main road by day, quiet hair dryer at 1 m distance to ear 65 dBA Bad risk of heart circulation disease at constant impact is possible 60 dBA Noisy lawn mower at 10 m distance 55 dBA Low volume of radio or TV at 1 m distance, noisy vacuum cleaner at 10 m distance 50 dBA Refrigerator at 1 m distance, bird twitter outside at 15 m distance 45 dBA Noise of normal living; talking, or radio in the background 40 dBA Distraction when learning or concentration is possible 35 dBA Very quiet room fan at low speed at 1 m distance 25 dBA Sound of breathing at 1 m distance 0 dB Auditory threshold
 *) A small frequency region makes high volume; see: Loudspeaker efficiency versus sensitivity “Amateurs” frequently ask about the high dB values from a siren. They are satisfied with each mentioned dB value. But they are not interested on the substantial distancefrom the noise source. That shows that they are just “dummies”. Rated sound is not specified in phones, but increasingly in dB (A). If in the measurement of the noise the distance to the measurement microphone is not specified, this information is worthless. This unfortunately happens quite often. The sound power level in dB ist not the sound pressure level (SPL) or the sound intensity level! This information is often not understood or seems to be confusing.

From a dB-A measurement no accurate description of the expected noise volume is possible.

Table of the
Threshold of pain

What is the pain threshold?

You can find the following rounded values in various audio articles and books:

 Sound pressure level Lp Sound pressure p 140 dBSPL 200 Pa 137.5 dBSPL 150 Pa 134 dBSPL 100 Pa 130 dBSPL 63 Pa 120 dBSPL 20 Pa
 The threshold of pain is known in acoustics as the lowest strength of a stimulus, that is perceived by the ear as painful. Because of the different sensitivity of people it cannot be given an accurate value.
 Permissible Exposure Time Guidelines ? Sound Pressure Level – SPL How long can a person endure a certain noise level before hearing impairment occurs?
 Accepted guidelines for recommended permissible exposure time for continuous time weighted average noise, according to NIOSH-AINSI and CDC. For every 3 dB sound pressure level (SPL) over 85 dB, the permissible exposure time is cut in half ? before damage to our hearing can occur. NIOSH = National Institute for Occupational Safety and Health and CDC = Centers for Disease Control and Prevention. OSHA = Occupational Safety and Health Administration. This may not represent a worldwide view of the subject. Noise is an increasing public health problem and can have the following adverse health effects: hearing loss, sleep disturbances, cardiovascular and psychophysiological problems, performance reduction, annoyance responses, and adverse social behaviour. A person feels and judges sound events by exposure time, spectral composition, temporal structure, sound level, information content and subjective mental attitude.
 Simply enter the value to the left or the right side. The calculator works in both directions of the ? sign.
 Sound pressure level 94 dB + dB ? Permissible exposure time minutes
 Integration times of hearing: ca. 100 µs to 3 ms / 10 ms (sum localization) ca. 5 ms – 10 ms: echo threshold / masking ca. 10 ms coupling width ca. 50 ms pitch detection (recognition) ca. 250 ms sound smearing / quasi-stationary processes.

The Psychoacoustic Loudness

 Note: Which increase corresponds to a doubling of the sound? An increase of the sound level by 3 dB corresponds to a doubling (factor = 2) of sound intensity. An increase of the sound level by 6 dB corresponds to a doubling of the sound pressure. An increase in the sound level by 10 dB corresponds to the sensation of double the “volume”. The subjective perceived “volume” or “loudness level” and the artificial term “loudness” has not to be mixed with the objective measure of sound pressure as sensation size of the human sense of hearing. The sound pressure as a sound field size is not the same as the sound intensity as sound energy size. Psychoacousticians tell us that a level increase of 10 dB should result in an impression of doubling the loudness (volume). If you have 6 violins as the initial source, then you need 10 times the violins, or 60 violins to double the psychoacoustic volume (loudness).
 Half loudness ? level     ?10 dB Double loudness ? level     +10 dB Half sound pressure ? level ?6 dB Double sound pressure ? level      +6 dB Half power ? level ?3 dB Double power: ? level      +3 dB four times power ? level +6 dB Ten times power ? level     +10 dB Double distance ? level ?6 dB Double sources (Double power) ? +3 dB
 Note: For example, when the sound system with spaced loudspeakers delivers twice the sound pressure as “one” amplifier,the fourfold power is required. So you need to double the “sound pressure” for example, four parallel amplifiers of the same design. Frequently one hears the novice question: How much more speaker power do you need for double the “volume” (loudness)? This takes about ten times the power.

Sound Level Comparison Chart and the Ratios

 Table of sound level dependence and the change of the respective ratio to subjective volume (loudness), objective sound pressure (voltage), and sound intensity (acoustic power) How many decibels (dB) change is double, half, or four times as loud? How many dB to appear twice as loud (two times)? Here are all the different ratios. Ratio means “how many times” or “how much” … Doubling of loudness.
 Subjectively perceived loudness (volume), objectively measured sound pressure (voltage), and theoretically calculated sound intensity (acoustic power)
 Level Change Volume Loudness Voltage Sound pressure Acoustic Power Sound Intensity +40 dB 16 100 10000 +30 dB 8 31.6 1000 +20 dB 4 10 100 +10 dB 2.0 = double 3.16 = ?10 10 +6 dB 1.52 times 2.0 = double 4.0 +3 dB 1.23 times 1.414 times = ?2 2.0 = double – – – – ±0 dB – – – – – – – – 1.0 – – – – – – – – – – – 1.0 – – – – – – – – – – – – 1.0 – – – – – ?3 dB 0.816 times 0.707 times 0.5 = half ?6 dB 0.660 times 0.5 = half 0.25 ?10 dB 0.5 = half 0.316 0.1 ?20 dB 0.25 0.100 0.01 ?30 dB 0.125 0.0316 0.001 ?40 dB 0.0625 0.0100 0.0001 Log. size Psycho size Field size Energy size dB change Loudness multipl. Amplitude multiplier Power multiplier

The psycho-acoustic volume or loudness is a subjective sensation size.

 Is a 10 dB or 6 dB sound level change for a doubling or halving of the loudness (volume) correct? About the connection between sound level and loudness, there are various theories. Far spread is still the theory of psycho-acoustic pioneer Stanley Smith Stevens, indicating that the doubling or halving the sensation of loudness corresponds to a level difference of 10 dB. Recent research by Richard M. Warren, on the other hand leads to a level difference of only 6 dB. *) This means that a double sound pressure corresponds to a double loudness. The psychologist John G. Neuhoff found out that for the rising level our hearing is more sensitive than for the declining level. For the same sound level difference the change of loudness from quiet to loud is stronger than from loud to quiet. It is suggested that the sone scale of loudness reflects the influence of known experimental biases and hence does not represent a fundamental relation between stimulus and sensation. Citation: When known experimental biases were eliminated, half loudness was equal to half sound pressure level (?6 dB) from 45 to 90 dB. It follows that the determination of the volume (loudness) which is double as loud should not be dogmatically defined. More realistic is the claim:
 A doubling of the sensed volume (loudness) is equivalent to a level change approximately between 6 dB and 10 dB.
 Question: What is the standard distance to measure sound pressure level away from equipment? There is really no standard distance for measuring dB (decibels). It depends on the size of the sound source and the sound pressure level.

Sound pressure is not intensity

 Differentiate: Sound pressure p is a “sound field size” and sound intensity I is a “sound energy size“. In teachings these terms are not often separated sharply enough and sometimes are even set equal. But I ~ p2.

Changing of sound power with distance is nonsense

 Question: How does the sound power decrease with distance”? Answer: “April fool – The sound power does not decrease (drop) with distance from the sound source.” Levels of sound pressure and levels of sound intensity decrease equally with the distance from the sound source. Sound power or sound power level has nothing (!) to do with the distance from the sound source. Thinking helps: A 100 watt light bulb has in 1 m and in 10 m distance really always the same 100 watts, which is emitted from the lamp all the time. Watts don’t change with distance. A frequent question: “Does the sound power depend on distance?” The clear answer is: “No, not really.” We consider sound fields in air which are described by the scalar quantity p (sound pressure) and the vector quantity v (sound velocity) as a sound field quantity.
 Note: The radiated sound power (sound intensity) is the cause and the sound pressure is the effect, where the sound engineer is particularly interested in the effect.
 Acousticians and sound protectors (noise fighters) need the sound intensity (acoustic intensity). As a sound designer you don’t need that sound energy size. The eardrums of our hearing and the diaphragms of the microphones are effectively moved by the sound pressure or the sound pressure level. Who is involved in audio engineering, should care less about the cause of intensity, power and energy, but better care on the effect of the sound pressure and the sound level (sound pressure level SPL) on the eardrums and the microphones, and the corresponding audio voltage or its voltage level.

Ratio magnitudes and levels

 The decibel is defined as a 20 times logarithm of a ratio of linear sizes to each other and as a 10 times logarithm of a ratio of quadratic sizes to each other. Ratios of electric or acoustic sizes, such as electric voltage and the sound pressure is referred to as ratios (factors), such as reflection factor. Ratios of square sizes to one another, such as power and energy are called grades, such as efficiency. Logarithmically ratios of electric or acoustic sizes of the same unit, we express as measures such as transfer factor, or level, such as sound pressure level. Levels are measured in decibels – dB in short.
 If the output voltage level is 0 dB, that is 100%, the level of ?3 dB is equivalent to 70.7% and the level of ?6 dB is equivalent to 50% of the initial output voltage. This applies to all field sizes; e.g. sound pressure. If the output power level is 0 dB, that is 100%, the level of ?3 dB is equivalent to 50% and ?6 dB is equivalent to 25% of the initial output power. This applies to all energy sizes; e.g. sound intensity. Try to understand this.

Conversion of sound pressure to sound power and vice versa

 The sound pressure changes depending on the environment and the distance from the sound source. In contrast, the sound power of a sound source is location-independent. Formulas for conversion: Acoustical power (sound power) Pac = I × Ain watts Sound intensity I = peff2 / Z0 in W/m2 = Pac / Ain W/m2 Perfused area A = 4 × ? × r2 in m2 Distance measurement point from the sound source r in meters (has only meaning with sound pressure, not with sound power) Acoustic impedance of air Z0 = 413 N·s/m3 at 20 °C Sound pressure peff in Pa = N/m2 In point-like sound sources spherical areas A shall be inserted. Depending on the arrangement following sections are taken into account: Solid sphere – sound source anywhere in the room, Q = 1 Hemisphere – sound source on the ground, Q = 2 Quarter Sphere – sound source on the wall, Q = 4 Eighth sphere – sound source in the corner, Q = 8 Q = direction factor and area A = (4 × ? × r2) / Q
 A typical question: “What is the dB volume of a symphony orchestra?” Answer: “It really depends on the distance of the listener to the orchestra.” To name the distance is often “forgotten”. They want to hear only a decibel number. But only a dB number is really senseless.
 The constant unsureness is the answer to the question: “How many decibels (dB) are doubling a sound”? or “What is twice the sound?” Answer: Doubling means the “factor 2”. What does doubling of a “sound” mean? Doubling the (sound) intensity is obtained by an increase of the (sound intensity) level of 3 dB. Doubling the sound pressure is obtained by an increase of the (sound pressure) level of 6 dB. Doubling the loudness feeling is obtained by an increase of the (loudness) level of about 10 dB.
 Simple rule of thumb: When working with power, 3 dB means double (twice) the factor and 10 dB means 10-fold. When working with voltage or current, 6 dB means double (twice) the factor and 20 dB means 10-fold.
 Some information about Hearing Level (HL) Pure-tone audiometric thresholds are expressed in dB HL
 Frequency dB SPL dB HL 250 Hz +15.0 0.0 500 Hz +9.0 0.0 1000 Hz +3.0 0.0 000 Hz ?3.0 0.0 4000 Hz ?4.0 0.0 8000 Hz +13.0 0.0
 In sound engineering there is no power matching or impedance matching. In audio we use only voltage bridging or high impedance bridging. Please read this here: “8 Ohm Output” and “150 Ohm Input” ? What is that?