SOUND LEVELS, (Power, Intensity, Pressure)

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Nov 13, 2010, 6:54:08 PM11/13/10

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http://www.engineeringpage.com/technology/noise/levels.html

What is sound

Sound can generally by defined as vibrating waves in elastic media. These waves transfer energy without permanently transferring mass. Elastic media are gases, vapors, liquids and solids.
The human ear is capable of hearing vibrations in air in the frequency range of 20 to 20000 Hz. Underneath 20 Hz one speaks of intra-sound, above 20000 Hz of ultra-sound.

A human ear actually perceives the effective sound pressure level. This is a scalar that does not contain directional information. Direction estimation is done by the brain by evaluation of the time difference between the signals of both ears. The time difference occurs when a longitudinal sound wave passes the two ears under an angle.

So both scalars and vectors play a role in the technical representation of sound.

Types of waves

Waves progress in elastic media. The type of wave depends on the medium. In acoustics the most important types are the longitudinal wave and the bending wave.
Sound in air is a longitudinal wave. The face of the wave is normally flat, but can be spherical if it is caused by a point source. Bending waves are important for structure born sound. Bending waves progress in walls and plates. These bring the air in motion, causing radiation of sound. Other types of waves are dilatation waves and transverse waves.
An attractive visualisation of longitudinal and transverse waves can be found at The University of Messina

The speed of a longitudinal wave can be calculated:
speed of sound

in which:
c = speed of sound in m/s
p = average pressure in Pa
= density in kg/m³
= specific heat ratio

For bending waves the formula is:

with:
E = modulus of elasticity in Pa
d = thickness of the plate in m
= surface mass of the plate in kg/m²

f = frequency in Hz

The formula shows a wave speed that is a function of the frequency. High frequency waves will travel faster than low frequency waves (dispersion). This can be observed at railways, when a train is coming the high frequency waves will travel faster and arrive first.

Sound power, intensity and pressure

Progressing sound can be represented by the sum of different sinus shaped waves. In an open field sound is stronger near the source and weaker further away as the energy of the source is distributed over a larger area. Both the sound intensity level and associated sound pressure level will be lower further away.

Underneath it is explained how these can be quantified.

Sound Power

A noise source radiates a certain amount of energy per unit of time. If one draws an area where the surface is perpendicular to direction of the energy flow and there are no losses of energy between the source and the surface, conservation of energy leads to:

or, if a surface that was not perpendicular was chosen:

In a lot of cases the intensity can be taken as evenly distributed over the surface. Many technical calculations are made like this, for example a sphere around a point source.

The symbols:
P = Sound Power in Watts
I = Sound Intensity in W/m²
S = Surface in m²

Sound Intensity

The intensity of sound is by definition the average power that is transmitted in the direction of progression, so intensity is a vector: it possesses magnitude and direction. For a longitudinal wave with a flat wave front the relationship between sound pressure and intensity can be proven to be:
sound intensity

with:
= effective sound pressure

The effective sound pressure is the root mean squared value (RMS) of the signal:

Sound Levels and dB

The human ear can perceive sound pressure over a very large range. The threshold of hearing at a frequency of 1000 Hz is p_eff = 2.10^-5 Pa. This threshold of hearing can be reproduced in a laboratory quite well and was chosen as the reference value.
Above p_eff = 100 Pa is painful.

The figures for Sound Power can range from 10^-9 W, for a whispering voice to 10⁶ W for a jet engine with afterburner.

These figures are not very handy, so the logaritmic scale was introduced. Using a logaritmic scale requires reference values. These reference values are (ISO 1683-2):
P_ref = 10^-12 W
I_ref = 10^-12 W/m²
p_ref = 2.10^-5 Pa (=N/m²)

Using these the definition of the sound levels are (all in dB):
Sound Power Level:

Sound Intensity Level:

Sound Pressure Level:

These values for these acoustic parameters were taken with care to obtain simple relationships for atmosperical air. The numerical value of sound pressure level and sound intensity level are the same as:
sound intensity and pressure relationship

The last term has the value 0.13 for atmospherical air and thus can be neglected.
This makes SPL = L_I.

Relationship Sound Power level and Sound Pressure Level

So the relationship between sound power level, sound pressure level and the surface is:

http://en.wikipedia.org/wiki/Sound_pressure

Sound pressure

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Sound measurements
Sound pressure p, SPL
Particle velocity v, SVL
Particle displacement ξ
Sound intensity I, SIL
Sound power P_ac
Sound power level SWL
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c
Audio frequency AF v • d • e

Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure p is the pascal (symbol: Pa).

Sound pressure diagram: 1. silence, 2. audible sound, 3. atmospheric pressure, 4. instantaneous sound pressure

Sound pressure level (SPL) or sound level is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in decibels (dB) above a standard reference level. The commonly used "zero" reference sound pressure in air is 20 µPa RMS, which is usually considered the threshold of human hearing (at 1 kHz).

[hide]

[edit] Instantaneous sound pressure

The instantaneous sound pressure is the deviation from the local ambient pressure p₀ caused by a sound wave at a given location and given instant in time.

The effective sound pressure is the root mean square of the instantaneous sound pressure over a given interval of time (or space).

Total pressure p_total is given by:

$p_{total} = p_{0} + p_{osc} \,$

where:

p₀ = local ambient atmospheric (air) pressure,

p_osc = sound pressure deviation.

[edit] Intensity

In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity. Together they determine the acoustic intensity of the wave. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity

$\vec{I} = p \vec{v}$

[edit] Acoustic impedance

For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the transmission medium.

The acoustic impedance is given by

p = vAZ

where

Z is acoustic impedance, sound impedance, or characteristic impedance, in Pa·s/m

v is particle velocity in m/s

I is acoustic intensity or sound intensity, in W/m²

A is surface area in m²

[edit] Particle displacement

Sound pressure p is connected to particle displacement (or particle amplitude) ξ by

$\xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} \,$ .

Sound pressure p is

$p = \rho c \omega \xi = Z \omega \xi = { 2 \pi f \xi Z} = \frac{a Z}{\omega} = c \sqrt{\rho E} = \sqrt{\frac{P_{ac} Z}{A}} \,$ ,

normally in units of N/m² = Pa.

where:

Symbol	SI Unit	Meaning
p	pascals	sound pressure
f	hertz	frequency
ρ	kg/m³	density of air
c	m/s	speed of sound
v	m/s	particle velocity
ω = 2 · π · f	radians/s	angular frequency
ξ	meters	particle displacement
Z = c • ρ	N·s/m³	acoustic impedance
a	m/s²	particle acceleration
I	W/m²	sound intensity
E	W·s/m³	sound energy density
P_ac	watts	sound power or acoustic power
A	m²	Area

[edit] Distance law

When measuring the sound created by an object, it is important to measure the distance from the object as well, since the sound pressure decreases with distance from a point source with a 1/r relationship (and not 1/r², like sound intensity).

The distance law for the sound pressure p in 3D is inverse-proportional to the distance r of a punctual sound source.

$p \sim \dfrac{1}{r} \,$

If sound pressure $p_1\,$ , is measured at a distance $r_1\,$ , one can calculate the sound pressure $p_2\,$ at another position $r_2\,$ ,

$\frac{p_2} {p_1} = \frac{r_1}{r_2} \,$

$p_2 = p_{1} \cdot \dfrac{r_1}{r_2} \,$

The assumption of 1/r² with the square is here wrong. That is only correct for sound intensity.

$I \sim {p^2} \sim \dfrac{1}{r^2} \,$

The sound pressure may vary in direction from the source, as well, so measurements at different angles may be necessary, depending on the situation. An obvious example of a source that varies in level in different directions is a bullhorn.

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 is not equivalent to pressure.

[edit] Sound pressure level

Sound pressure level (SPL) or sound level L_p is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in decibels (dB) above a standard reference level.

$L_p=10 \log_{10}\left(\frac{{p_{\mathrm{{rms}}}}^2}{{p_{\mathrm{ref}}}^2}\right) =20 \log_{10}\left(\frac{p_{\mathrm{rms}}}{p_{\mathrm{ref}}}\right)\mbox{ dB} ,$

where p_ref is the reference sound pressure and p_rms is the rms sound pressure being measured.^[1]^{[note 1]}

Sometimes variants are used such as dB (SPL), dBSPL, or dB_SPL. These variants are not recognized as units in the SI.^[2]

The unit dB (SPL) is often abbreviated to just "dB", which can give the erroneous impression that a dB is an absolute unit by itself. The commonly used reference sound pressure in air is p_ref = 20 µPa (rms), which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away). Most sound level measurements will be made relative to this level, meaning 1 pascal will equal 94 dB SPL. In other media, such as underwater, a reference level of 1 µPa is more often used.^[3] These references are defined in ANSI S1.1-1994.^[4]

The lower limit of audibility is therefore defined as 0 dB, but the upper limit is not as clearly defined. While 1 atm (191 dB) is the largest pressure variation an undistorted sound wave can have in Earth's atmosphere, larger sound waves can be present in other atmospheres, or on Earth in the form of shock waves.

Ears detect changes in sound pressure. Human hearing does not have a flat spectral sensitivity (frequency response) relative to frequency versus amplitude. Humans do not perceive low- and high-frequency sounds as well as sounds near 2,000 Hz, as shown in the equal-loudness contour. Because the frequency response of human hearing changes with amplitude, three weightings have been established for measuring sound pressure: A, B and C. A-weighting applies to sound pressures up to 55 dB SPL, B-weighting applies to sound pressures between 55 and 85 dB SPL, and C-weighting is for measuring sound pressure above 85 dB SPL.^{[citation needed]}

In order to distinguish the different sound measures a suffix is used: A-weighted sound pressure level is written either as dB_A or L_A. B-weighted sound pressure level is written either as dB_B or L_B, and C-weighted sound pressure level is written either as dB_C or L_C. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dB_L or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.

[edit] Multiple sources

The formula for the sum of the sound pressure levels of n incoherent radiating sources is

$L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(\frac{{p_1}^2 + {p_2}^2 + \cdots + {p_n}^2}{{p_{\mathrm{ref}}}^2}\right) = 10\,\cdot\,{\rm log}_{10} \left(\left({\frac{p_1}{p_{\mathrm{ref}}}}\right)^2 + \left({\frac{p_2}{p_{\mathrm{ref}}}}\right)^2 + \cdots + \left({\frac{p_n}{p_{\mathrm{ref}}}}\right)^2\right)$

From the formula of the sound pressure level we find

$\left({\frac{p_i}{p_{\mathrm{ref}}}}\right)^2 = 10^{\frac{L_i}{10}},\qquad i=1,2,\cdots,n$

This inserted in the formula for the sound pressure level to calculate the sum level shows

$L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + \cdots + 10^{\frac{L_n}{10}} \right)\,{\rm dB}$

[edit] Examples of sound pressure and sound pressure levels

http://en.wikipedia.org/wiki/Sound_power_level

Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level. While sound pressure level is given in decibels SPL, or dB SPL, sound power is given in dB SWL. The dimensionless term "SWL" can be thought of as "sound watts level,"^[1] the acoustic output power measured relative to a very low base level of watts given as 10^-12 or .000000000001 watts. As used by architectural acousticians to describe noise inside a building, typical noise measurements in SWL are very small, less than 1 watt of acoustic power.^[1]

The sound power level of a signal with sound power W is:^[2] ^[3] $L_\mathrm{W}=10\, \log_{10}\left(\frac{W}{W_0}\right)\ \mathrm{dB}$

where W₀ is the 0 dB reference level:

$W_0=10^{-12}\ \mathrm{W}$

The sound power level is given the symbol L_W. This is not to be confused with dBW, which is a measure of electrical power, and uses 1 W as a reference level.

In the case of a free field sound source in air at ambient temperature, the sound power level is approximately related to sound pressure level (SPL) at distance r of the source by the equation

$L_\mathrm{p} = L_\mathrm{W}+10\, \log_{10}\left(\frac{S_0}{4\pi r^2}\right)$

where $S_0 = 1\ \mathrm{m}^2$ .^[1] This assumes that the acoustic impedance of the medium equals 400 Pa·s/m.

[edit] Table: Sound power level and sound power of some sound sources

Situation and sound source	sound power P_ac watts	sound power level L_w dB re 10^-12 W
Rocket engine	1,000,000 W	180 dB
Turbojet engine	10,000 W	160 dB
Siren	1,000 W	150 dB
Heavy truck engine or loudspeaker rock concert	100 W	140 dB
Machine gun	10 W	130 dB
Jackhammer	1 W	120 dB
Excavator, trumpet	0.3 W	115 dB
Chain saw	0.1 W	110 dB
Loud speech	0.001 W	90 dB
Usual talking, Typewriter	10⁻⁵ W	70 dB
Refrigerator	10⁻⁷ W	50 dB
(Auditory threshold at 2.8 m)	10^-10 W	20 dB
(Auditory threshold at 28 cm)	10^-12 W	0 dB

The Trumpet and excavator both have the same sound power of 0.3 watts, but may be judged psychoacoustically to be different levels. As noise is unwanted sound the trumpet can be perceived to be acceptable when listened to as music but at the same sound power level may be perceived to be noisy if one is trying to sleep.

One of the advantages of expressing the noise level of a source in terms of its power level is that one does not have to note any distance from the source.

[edit] References

^ ^a ^b ^c Chadderton, David V. Building services engineering, pp. 301, 306, 309, 322. Taylor & Francis, 2004. ISBN 0415315352
^ Sound Power, Sound Intensity, and the difference between the two - Indiana University's High Energy Physics Department
^ Georgia State University Physics Department - Tutorial on Sound Intensity

[edit] External links

http://www.usmotors.com/products/ProFacts/sound_power_and_sound_pressure.htm

Sound Power and Sound Pressure

"Sound power" and "sound pressure" are two distinct and commonly confused characteristics of sound. Both share the same unit of measure, the decibel (dB), and the term "sound level" is commonly substituted for each. However, to understand how to measure and specify sound, the Motor system designer must first understand the difference between these properties.

To obtain the maximum benefit from sound power level (Lw) ratings, an engineer must understand what Lw ratings represent and how to apply them properly. For the design engineer who is not yet familiar with the techniques of applying Lw ratings, this article may serve as a brief introduction.

Sound Power Ratings

Sound power is the acoustical energy emitted by the sound source, and is an absolute value. It is not affected by the environment.

Motor Lw ratings are obtained from the determination of sound power levels generated by a motor when it is operated at no load. These sound power levels are obtained in accordance with IEEE 85. What is heard is a sound pressure level that is determined, for any particular location, by many factors, including size of the room, nature of its walls, ceilings, furnishings, etc. The pressure level at the point of hearing is also related to the distance from the sound source. The motor is the starting point, and when proper and accurate consideration is given to the other components of the system, sound power level ratings in octave bands will allow calculation of the resulting sound pressure levels in the space.

Sound power levels are connected to the sound source and independent of distance. Sound powers are indicated in decibel.

L_w = 10 log (W / W₀) where:

W₀ = reference power (W)

The normal reference level is 10^-12 W, which is the lowest sound persons of excellent hearing can discern. Sound power is measured as the total sound power emitted by a source in all directions in watts (joules / second).

Sound Pressure Level

Sound pressure is a pressure disturbance in the atmosphere whose intensity is influenced not only by the strength of the source, but also by the surroundings and the distance from the source to the receiver. Sound pressure is what our ears hear, what sound meters measure ... and what ultimately determines whether a design achieves quality sound.

The sound pressure level in a space may be estimated when sufficient information is available from the Lw of motor and the acoustical characteristics of the space. A proper acoustical calculation requires the use of the motor Lw stated separately for each of the eight octave bands. Each octave band level is usually different, and the room acoustical characteristics also vary with frequency.

Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level. Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors.

Sound Pressure Level (SPL) $= 20 \log \frac{p}{p_{0}} = 10 \log (\frac{p}{p_{0}})^{2}$ , where p_o = 2x10^-5 N/m².

p = root mean square pressure (N/m²)

The usual reference level p_o is 20x10^-6 N/m². Note that the noise from motors is documented in sound power level. "Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than 10^-9 of atmospheric pressure or about 20x10^-5 N/m²at 1000 Hz. "Threshold of pain'' corresponds to a pressure 10⁶ times greater, but still less than 1/1000 of atmospheric pressure. Because of the wide range, sound pressure measurements are made on a logarithmic scale (decibel scale).

Relating Power To Pressure

Equipment sound power ratings are determined in an acoustics laboratory, usually by the manufacturer. Specific standards qualify testing facilities and methods to promote data uniformity and objective comparisons of different units across the industry.

By contrast, sound pressure can be measured in an existing space with a sound meter, or predicted for a space not yet constructed by means of an acoustical analysis. Since the only accurate sound data a manufacturer can provide is expressed as sound power, the challenge of designing for quality sound is to examine the effect of environmental factors.

An Illuminating Analogy

The following comparison of sound and light may help illustrate the distinction between these terms. Think of sound power as the wattage rating of a light bulb; both measure a fixed amount of energy. Sound pressure corresponds to the brightness in a particular part of the room; both can be measured with a meter and the immediate surroundings influence the magnitude of each. In the case of light, brightness is more than a matter of bulb wattage. Asking for a 90 dBA motor is a lot like asking for a “light:” you don’t know what you are going to get. Most of us are much more familiar with light than sound. If someone says he has a 100-watt light bulb, you have some idea of the candlepower available, but if you want to read by the light, you want to know the light intensity level at the reading location. To determine the light intensity level you would need to know:

“How far away is the light?” If the light is a mile away, it is not much use. The analogous sound question is “How far away is the motor?”
“Is the light outdoors?” With no walls to reflect the light, all but the direct light radiates out into the free field of space. The analogous sound question is “Is the motor outdoors?”
“Are the room walls reflective if the light is not outdoors?” A room covered with black velvet would not reflect much light regardless of its size. The analogous sound question is “How reverberant are the walls?”

Motor dBA Rating

The term dBA applies to sound pressure. The sound pressure immediately around a motor depends on a number of variables. Sound pressure can only be calculated from the motor sound power rating when using known variables. Motor manufacturers indicate the noise level of their products by sound pressure levels expressed in dBA. These figures refer to the sound pressure levels that should be experienced by an observer at a certain distance from the motor in a given environment, which is generally assumed to be a free field. These values should only be used to compare noise levels of similar types of motors at the same distance, and in the same environment. Do not assume that the dBA levels on the performance data will in any way be similar to those achieved in practice. Depending on circumstances, they can be substantially exceeded.

Sound Power to Pressure Conversion Rule of Thumb

TYPICAL FREE FIELD SOUND PRESSURE
VERSUS SOUND POWER LEVELS - IN dB

FRAME SERIES	POWER LEVEL	PRESSURE LEVEL @ 3 FT	PRESSURE LEVEL @ 5 FT
140	X	X - 7.8	X - 10.6
180	X	X - 8.0	X - 10.8
210	X	X - 8.2	X - 10.9
250	X	X - 8.4	X - 11.1
280	X	X - 8.8	X - 11.4
320	X	X - 9.0	X - 11.6
360	X	X - 9.2	X - 11.8
400	X	X - 9.5	X - 12.0
440	X	X - 10.9	X - 12.4
5000	X	X - 10.6	X - 12.8
5800	X	X - 11.6	X - 13.7
6800	X	X - 11.9	X - 13.9
8000	X	X - 12.5	X - 14.7

Calculating Sound Pressure

Sound instruments measure only sound pressure; this pressure varies depending on the surroundings. To calculate sound pressure from sound power, one must consider all the variables that affect sound pressure. The relationship between sound power level (sound energy emitted by the motor and sound pressure (what is heard) at a specific location.

Human Response

Ear sensitivity varies with frequency. A low frequency sound at a certain power does not seem as loud as a higher frequency sound of the identical power. To account for this difference, a weighting scale has been developed. Sound power levels adjusted by this specific weighting scale are called A-weighted. Sound power levels in eight octave bands are calculated to a single A-weighted sound power number, LWA.

Free Field Ratings

Because one environment, a free field, can be easily defined, it is sometimes used to specify desired sound pressure levels. If a motor is placed on the ground in a large open field, all of its sound radiates out in a hemispherical free field with no sound reflected back. These conditions are fully defined, and it is possible to convert motor sound power to sound pressure at a specified distance. As distance from the motor increases, sound pressure decreases; so it is important to include distance from the motor when asking for a dBA rating. If you specify a hemispherical free field but do not specify a distance, it is possible to make a loud motor appear quieter by calculating its sound pressure level at a distance farther away from the motor. For example, Motor A calculates to 90 dBA at a distance of 3 m (10 ft) in a hemispherical free field. Another motor, Motor B, with a sound power level 12 dB higher than Motor A, will also calculate to 90 dBA, but at 12 m (40 ft) from the motor!

Multiple Sources

Two equal sources produce a 3 dB increase in sound power level. Two equal sources produce a 3 dB increase in sound pressure level, assuming no interference. Two 80 dB sources add to produce an 83 dB SPL.

http://www.engineeringtoolbox.com/sound-power-intensity-pressure-d_57.html

http://www.tutorvista.com/physics/sound-pressure-level

Sound Pressure Level

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Introduction to sound pressure level:

Every one of us is fond of music and many of us like to hear some music every time. Well, how many of us know that it is the variation of sound that we are experiencing without any physical feeling of the sound?

What is a sound?

This might be one of the many basic questions that you were asking you elder ones while you were young and most of us might get kicked by them because of the reason why they didn’t have any answer to tell.

Actually what might be the sound? Sound is defined to as the wave that produced mechanically due to the pressure oscillation through solid, liquid and gas. The wave must be in a level sufficient to hear and also it must be in a range that can be heard. The feeling of hearing sensation is occurred with the help of the organs that helps in hearing; ear with the help of vibrations.

Sound Pressure

The sound pressure is the deviation in atmospheric pressure that is caused by a sound wave. There are instruments available for measuring the sound pressure also. This may be a hydrophone in water and a microphone in the air. The unit for sound pressure in SI is Pascal. This can be denoted using p.

Sound Pressure Level and Instantaneous Sound Pressure

Sound pressure level:

Sound pressure level can also be called as sound level. It is the logarithmic pressure of effective sound pressure of a sound, relative to the reference value and it is measured in decibels (dB).

Instantaneous sound pressure:

This can be defined to as the deviation caused by a sound wave from a local ambient pressure p₀ at a particular location in a unit time.

The total pressure can be calculated by using the equation

p_total= p₀ +p_osc

where the p₀ is defined as the local ambient pressure and p_osc is the sound deviation pressure.

An effective sound pressure can be found out by taking the root mean square of the instantaneous sound pressure in a given interval of time.

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