Sound Pressure Level and Power

December 2, 2018 | Author: nicklingatong | Category: Loudspeaker, Decibel, Sound, Resonance, Logarithm

Description

phon A unit of apparent loudness, equal in number to the intensity in decibels of a 1,000-hertz tone perceived to be as loud as the sound being measured. Sound Intensity Sound Intensity is the Acoustic or Sound or Sound Power (W) per unit area. The SI-units for Sound Intensity are 2  W/m .

Sound Intensity Level The dynamic range of human hearing and sound intensity spans from 10 -12  W/m2  to 10 - 100 W/m2 . The highest sound intensity possible to hear is 10,000,000,000,000 times as loud as the quietest! quie test! This span makes the absolute value of the sound intensity impractical for normal use. A more convenient way to express the sound intensity is i s the relative logarithmic scale with reference to the lowest human hearable sound - 10 -12  W/m2 (0 dB). Note! In US a reference of  10 -13 watts/m2  are commonly used. The Sound Intensity Level can be expressed as: LI  = 10 log(I / I ref    ) (1) ref  where LI  = sound intensity level (dB) I = sound intensity (W/m2  ) -12  2  I ref  ref  = 10  - reference sound intensity (W/m  )

The logarithmic sound intensity level scale match the human sense of hearing. Doubling the intensity increases the sound level with 3 dB (10 log (2)).

Example - Sound Intensity The difference in intensity of 10 -8  watts/m2  and 10 -4 watts/m2  (10,000 units) can be calculated in decibels as  ΔLI  = 10 log( (10 -4 watts/m2  ) / (10 -12  watts/m2  ) ) - 10 log( ( 10 -8  watts/m2  ) / ( 10 -12  watts/m2  ) ) = 40 dB

Increasing the sound intensity by a factor of  • • • • •

10 raises its level by 10 dB 100 raises its level by 20 dB 1,000 raises its level by 30 dB 10,000 raises its level by 40 dB and so on

Note! Since the sound intensity level may be difficult to measure, it is common to use sound pressure

level measured in decibels instead. Doubling the Sound Pressure raises the Sound Pressure Level with 6  dB.

Loudness Sound intensity and feeling of loudness: • •

110 to 225 dB - Deafening  90 to 100 dB - Very Loud

• • • •

70 to 80 dB - Loud  45 to 60 dB - Moderate 30 to 40 dB - Faint  0 - 20 dB - Very Faint

Sound Power, Intensity and Distance to Source The sound intensity decreases with distance to source. Intensity and distance can be expressed as: I = Lw  / 4 π r 2  (2) where Lw  = sound power (W) π = 3.14 r = radius or distance from source (m)

Sound Intensity and Sound Pressure The connection between Sound Intensity and S ound Pressure can be expressed as: I = p2  / ρ c (3) where  p = sound pressure (Pa)  ρ = density of air (1.2 kg/m 3 at 20 oC) c = speed of sound (331 sound (331 m/s)

Sound Power  Sound power is the energy rate - the energy of sound per unit of time ( J/s, W in SI-units) from a sound source.

Sound Power Level Sound power can more practically be expressed as a relation to the threshold of hearing - 10 -12  W - in a logarithmic scale named Sound Power Level - Lw , expressed as Lw  = 10 log (N / N o  ) (1) where Lw  = Sound Power Level in Decibel  Decibel (dB) (dB) N = sound power (W) N o = 10 -12  - reference sound power (W).

Human hearable Sound Power spans from 10 -12  W to 10 - 100 W , a range of 10/10 -12  = 10 13. The table below indicates the Sound Power and the Sound Power Level from some common sources.

Source

Sound Power  -N(W )

Sound Power  Level - Lw  (dB) (re 10 -12  W )

Saturn Rocket

100,000,000

200

Turbo Jet Plane Engine

100,000

170

10,000

160

Inside jet engine test cell Jet Plane Take-off

1,000

150

Large centrifugal fan, 800.000 m3/h Turbo Propeller Plane at take-off

100

140

Axial fan, 100.000 m3/h Machine Gun Large Pipe Organ

10

130

Large chipping hammer  Symphonic orchestra Jet Plane from passenger ramp Heavy Thunder  Sonic Boom Small aircraft engine

1

120

Centrifugal van, 25.000 m3/h Accelerating Motorcycle Heavy Metal, Hard Rock Band Music Blaring radio Chain Saw Wood Working Shop Large air Compressor

0.1

110

Air chisel Subway Steel Wheels Magnetic drill press High pressure gas leak Banging of steel plate Drive gear  Car at Highway Speed Normal Fan Vacuum Pump Banging Steel Plate Wood Planer  Air Compressor  Propeller Plane Outboard motor  Loud street noise Power Lawn Mover  Helicopter

0.01

100

Cut-off saw Hammer mill Small air compressor  Grinder  Heavy diesel vehicle Heavy city traffic Lawn mover  Airplane Cabin at normal flight Kitchen Blender  Spinning Machines Pneumatic Jackhammer

0.001

90

Alarm clock Dishwasher

0.0001

80

Toilet Flushing Printing Press Inside Railroad Car  Noisy Office Inside Automobile Clothes Dryer  Vacuum Cleaner

0.00001

70

Large department store Busy restaurant or canteen Ventilation Fan Noisy Home Average Office Hair Dryer

0.000001

60

Room with window air conditioner  Office Air Diffuser  Quiet Office Average Home Quit Street

0.0000001

50

Voice, low Small Electric Clock Private Office Quiet Home Refrigerator  Bird Singing Ambient Wilderness Agricultural Land

0.00000001

40

Room in a quiet dwelling at midnight

0.000000001

30

Quiet Conversation Broadcast Studio Rustling leaves Empty Auditorium Whisper  Watch Ticking Rural Ambient

0.0000000001

20

Human Breath

0.00000000001

10

0.000000000001

0

The Decibel Decibel is a logarithmic unit used to describe physical values like the ratio of the signal level - power, sound pressure, voltage or intensity. The decibel can be expressed as: decibel = 10 log( P / P ref  ) where P = signal power (W) P ref  = reference power (W)

(1)

Sound Power Level Sound power is the energy rate - the energy of sound per unit of time (J/s, W in SI-units) from a sound source. Sound power can more practically be expressed as a relation to the threshold of hearing - 10 -12 W - in a logarithmic scale named Sound Power Level - Lw : Lw  = 10 log ( N / N o  ) (2) where Lw  = Sound Power Level in Decibel (dB) N = sound power (W) •

The lowest sound level that people of excellent hearing can discern has an acoustic sound power about 10-12 W, 0 dB The loudest sound generally encountered is that of a jet aircraft with a sound power of  105 W, 170 dB.

Sound Intensity Sound Intensity is the Acoustic or Sound Power (W) per unit area. The SI-units for Sound Intensity are W/m2. The Sound Intensity Level can be expressed as: LI  = 10 log( I / I ref  ) (3) where LI  = sound intensity level (dB) I = sound intensity (W/m2  )

I ref  = 10 -12  - reference sound intensity (W/m2  )

Sound Pressure Level The Sound Pressure is the force (N) of sound on a surface area (m 2) perpendicular to the direction of the sound. The SI-units for the Sound Pressure are N/m2 or Pa. The Sound Pressure Level: L p = 10 log( p2  / pref 2  ) = 10 log( p / pref  )2  = 20 log ( p / pref  ) where L p = sound pressure level (dB)  p = sound pressure (Pa)  pref  = 2 10 -5  - reference sound pressure (Pa) •

(4)

If the pressure is doubled, the sound pressure level is increased with 6 dB (20 log (2))

Sound Pressure The Sound Pressure is the force (N ) of sound on a surface area ( m2 ) perpendicular to the direction of the sound. The SI-units for the Sound Pressure are N/m2  or Pa. Sound is usually measured with microphones responding proportionally to the sound pressure - p. The power in a sound wave goes as the square of the pressure. (Similarly, electrical power goes as the square of the voltage.) The log of the square of x is just 2 log x, so this introduces a factor of 2 when we convert to decibels for pressures.

The Sound Pressure Level The lowest sound pressure possible to hear is approximately 2 10 -5  Pa (20 micro Pascal, 0.02 mPa), 2 ten billionths of a an atmosphere. It therefore convenient to express the sound pressure as a logarithmic decibel scale related to this lowest human hearable sound - 2 10 -5  Pa, 0 dB. The Sound Pressure Level: L p = 10 log( p2  / pref 2  ) = 10 log( p / pref  )2  = 20 log ( p / p ref  ) where L p = sound pressure level (dB)  p = sound pressure (Pa)  pref  = 2 10 -5  - reference sound pressure (Pa)

(1)

If the pressure is doubled, the sound pressure level is increased with 6 dB (20 log (2)). •

Recommended maximum sound pressure level in rooms with different activities.

The table below indicates the sound pressure level in decibel caused by some common sources.

Source

Sound Pressure Level (dB)

Threshold of Hearing

Quietest audible sound for  persons with excellent hearing under laboratory

0

conditions2) Quietest audible sound for persons under normal conditions

Virtual silence

10

Rustling leaves, quiet room

20

Noticeably Quit - Voice, soft whisper

Quiet whisper (1 m)

30

Home

40 Moderate

Quiet street

50

Loud - Unusual Background, Voice conversation 1 m

Conversation

60

Loud - Voice conversation 0.3 m

Inside a car  Car (15 m) Vacuum cleaner (3 m) Freight Train (30 m)

70

Loud singing

75

Loud - Intolerable for Phone Use

Automobile (10 m) Maximum sound up to 8 hour (OSHA criteria hearing conservation program) Pneumatic tools (15 m) Buses, trucks, motorcycles

80

(15 m) Motorcycle (10 m)

88

Food blender (1 m) Maximum sound up to 8 hour (OSHA1) criteria engineering or  administrative noise controls) Jackhammer (15 m) Bulldozer (15 m)

90

Subway (inside)

94 Very Loud

Diesel truck (10 m)

100

Lawn mower (1 m)

107

Pneumatic riveter (1 m)

115

Threshold of Discomfort

Large aircraft (150 m over  head)

110

Chainsaw (1 m)

117

Deafening, Human pain limit

Amplified Hard Rock (2 m) Siren (30 m)

120

Jet plane (30 m) Artillery Fire (3 m)

130

Short exposure can cause hearing loss

Military Jet Take-off (30

meter)

Sound Pressure Level and Power  Sound Pressure Level •

• •

``Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than of atmospheric pressure or about N/m at 1000 Hz. ``Threshold of pain'' corresponds to a pressure 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). Sound Pressure Level (SPL) , where SPL is proportional to the average squared amplitude.

N/m .

Sound Power

Total sound power emitted by a source in all directions. Measured in watts (joules / second).

Sound Power Level (PWL) =

, where

watts.

Sound Intensity •

Rate of energy flow across a unit area.

Sound Intensity Level (IL) =

, where

watts/meter .

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.

Room acoustics A - Introduction Much has been written in the popular and professional audio press about the acoustic treatment of rooms. The purpose of such treatment is to allow us to hear more of the loudspeaker and less of the room. I am convinced that a properly designed sound system can perform well in a great variety of rooms and requires only a minimum of room treatment if any at all.

To understand this claim let's look at the typical acoustic behavior of domestic size listening rooms, which have linear dimensions that are small compared to the 17 m wavelength of a 20 Hz bass tone, but are acoustically large when compared to a 200 Hz or 1.7 m wavelength midrange tone (G1 on the piano keyboard). Below 200 Hz the acoustics of different locations in the room are dominated by discrete resonances. Above 200 Hz these resonances become so tightly packed in frequency and space that the room behaves quite uniformly and is best described by its reverberation time RT60. Room treatment can be very effective above 200 Hz, but the same result may be obtained more aesthetically with ordinary furnishings, wall decoration, rugs on the floor and the variety of stuff  we like to surround ourselves with. How much treatment is needed, or how short the reverberation time should be, depends on the polar radiation characteristics of the loudspeaker. For my open baffle speaker designs a room becomes too dead when its RT60 falls below 500 ms. B - Loudspeaker directivity and room response When a loudspeaker is placed in a room we hear both its direct sound, i.e. the sound which arrives via the shortest path, and the room sound due to the resonances, reverberation and reflections caused by the boundaries of the room and the objects in it. The two sounds superimpose and influence our perception of timbre, timing and spatial location of the virtual sound source. Thus, the off-axis radiation of the speaker has great influence on the naturalness of sound reproduction even when you listen on-axis and the more so, the further you sit away from the speaker. Two basic and fundamentally different sources of sound are the monopole and the dipole radiator. The ideal monopole is an acoustically small pulsating sphere, and the ideal dipole is a back and forth oscillating small sphere. The monopole radiates uniformly into all directions, whereas the dipole is directional with distinct nulls in the plane vertical to its axis of oscillation. The 3-dimensional radiation or polar pattern of the monopole is like the surface of a basket ball, the dipole's is like two ping-pong balls stuck together. At +/-45 degrees off-axis the dipole response is L = cos(45) = 0.7 or 3 dB down, the monopole is unchanged with L = 1.

The graph above shows characteristic radiation patterns of different sound sources for very low, mid and high frequencies and with flat on-axis response. Practical loudspeakers are neither pure monopoles nor pure dipoles except at low frequencies where the acoustic wavelengths are large compared to the cabinet dimensions. The ideal monopole is omni-directional at all frequencies. Very few speaker designs on the consumer market approach this behavior. This type of speaker illuminates the listening room uniformly and the perceived sound is strongly influenced by the room's acoustic signature. The result can be quite pleasing, though, because a great deal of acoustic averaging of the sound radiated into every direction takes place. The speakers tend to disappear completely in the wide sound field. Unfortunately, the direct sound is maximally masked by the room sound and precise imaging is lost, unless the listening position is close to the speakers.

The typical box speaker, whether vented, band-passed or closed, is omni-directional at low frequencies and becomes increasingly forward-directional towards higher frequencies. Even when flat on-axis, the total acoustic power radiated into the room drops typically 10 dB (10x) or  more between low and high frequencies. The uneven power response and the associated strong excitation of low frequency room modes contributes to the familiar (and often desired :-( ) generic box loudspeaker sound. This cannot be the avenue to sound reproduction that is true to the original. The directional response of the ideal dipole is obtained with open baffle speakers at low frequencies. Note, that to obtain the same on-axis sound pressure level as from a monopole, a dipole needs to radiate only 1/3rd of the monopole's power into the room. This means 4.8 dB less contribution of the room's acoustic signature to the perceived sound. It might also mean 4.8 dB less sound for your neighbor, or that much more sound to you. Despite this advantage dipole speakers are often not acceptable, because they tend to be constructed as physically large panels that interfere with room aesthetics, and they seem to suffer from insufficient bass output, critical room placement and a narrow "sweet spot". These claims are true to varying degree depending on the specific design of a given panel loudspeaker. Because of the progressive acoustic short circuit between front and rear as the reproduced signal frequency decreases, the membrane of an open-baffle speaker has to move more air locally than the driver cone of a box speaker for the same SPL at the listening position. This demands a large radiating surface area, because achievable excursions are usually small for electrostatic or magnetic panel drive. The obtained volume displacement limits the maximum bass output. Non-linear distortion, though, is often much lower than for dynamic drivers. Large radiating area means that the panel becomes multi-directional with increasing frequency which contributes to critical room placement and listening position. If the open-baffle speaker is built with conventional cone type dynamic drivers of large excursion capability, then adequate bass output and uniform off-axis radiation are readily obtainable in a package that is more acceptable than a large panel, though not as small as a box speaker. Such speakers were built by Audio Artistry Inc. and a DIY project is described on this web site in the PHOENIX pages. This type of speaker has a much more uniform power response than the typical box speaker. Not only is its bass output in proportion to the music, because room resonance contribution is greatly reduced, but also the character of the bass now sounds more like that from real musical instruments. My hypothesis is that three effects combine to produce the greater bass clarity: 1 - An open baffle, dipole speaker has a figure-of-eight radiation pattern and therefore excites fewer room modes. 2 - Its total radiated power is 4.8 dB less than that of a monopole for the same on-axis SPL. Thus the strength of the excited modes is less. 3 - A 4.8 dB difference in SPL at low frequencies is quite significant, due to the bunching of the equal loudness contours at low frequencies, and corresponds to a 10 dB difference in loudness at 1 kHz. Thus, bass reproduced by a dipole would be less masked by the room, since a dipole excites fewer modes, and to a lesser degree, and since the perceived difference between direct sound and room contribution is magnified by a psychoacoustic effect., The off-axis radiation behavior of a speaker determines the degree to which speaker placement and room acoustics degrade the accuracy of the perceived sound. Worst in this respect is the

typical box speaker, followed by the large panel area dipole and the truly omni-directional designs. Least affected is the sound of the open-baffle speaker with piston drivers. (Ref.1) Often concern is expressed over the fact that the rear radiation from a dipole is out of phase with the front radiation, and that thus any sound reflected from a wall behind the speaker would cancel sound coming from the front of the speaker. Cancellation can only occur when direct and reflected sounds are exactly of opposite phase (180 degrees) and of the same strength. Since direct and reflected sounds travel paths of different length, they undergo different amounts of  phase shift. Thus, the phase and magnitude conditions for cancellation are given only at certain frequencies, if at all. At some other frequencies direct and reflected sounds will add. The same also applies to a monopole speaker in front of a wall. The only difference is in the frequencies for which addition and subtraction occur. The best remedy is to move the speaker away from the wall, or to make the wall as sound absorptive or diffusive as possible. ( FAQ31) Top

C - Room reverberation time T60 The Reverberation Time - T a - for a room is the time it takes before the sound pressure level has decreased with 60 dB after the sound source is terminated. The Reverberation Time - T a - can be calculated as:

Mean sound absorption coefficient

α m 0.35

Reverberation time is the single most important parameter describing a room's acoustic behavior. The following discussion might get a little technical but will illustrate how sound builds up and decays in a room and the effect it has upon clarity of reproduction. C1 - Sound waves between two walls Take the example of a speaker in a wall and a second wall at distance L in front of it. As the cone vibrates it will send out an acoustic wave which gets reflected back by the second wall, returns to the first wall, gets reflected again back to the second wall and so on. If the frequency of vibration is such that the distance L corresponds to half of a wavelength, then the cone movement is in phase with the reflected wave and the sound pressure keeps building up. Eventually an equilibrium is reached between the energy supplied by the cone movement and the energy absorbed by the two walls and the air in between.

This is a standing wave resonance or mode condition and if we change the frequency of cone vibration, we trace out the resonance curve that is typical for any simple system containing mass, compliance and energy loss. As frequency is increased another resonance occurs when L equals to a full wavelength, to 3/2 wavelengths, 4/2 and so on. The lowest possible frequency is f min = c / (2 L) Hz, where c=343 m/s (1) If the excitation is applied as a step function, then the sound pressure will rise from 10% to 90% of its steady-state level within a time Trise = 0.7 / BW (2) where BW is the width of the resonance curve in Hz at the half power (-3 dB) level. The SPL will decay to one millionth (-60 dB) of its full level after a time T60 = 2.2 / BW (3) The quality factor or Q of the resonance is Q = n f min / BW (4)

with n = 1, 2, 3, etc.

Example 1 L=25 ft (7.63 m), then f min = 343/(2*7.63) = 22.5 Hz and no resonance below this frequency. The next higher resonance will be at 45 Hz, then 67.5 Hz, 90 Hz, 112.5 Hz and so on. If we had measured Trise = 202 ms at 45 Hz, then from (2) BW = 0.7/0.202 = 3.5 Hz and T60 = 2.2/3.5 = 630 ms from (3). Q = 45/3.5 = 12.9 and if T 60 stays constant with increasing frequency, then Q increases, for  example Q = 112.5/3.5 = 32.1 C2 - Standing waves in a rectangular, rigid room In a rectangular room we have six surfaces and the number of possible standing waves is much larger than for the two wall example. The frequencies at which they can occur are calculated from f = ( c / 2 ) [ ( l / L ) 2 + ( w / W ) 2 + ( h / H ) 2 ]1/2

[Hz]

(5)

l, w, h = 0, 1, 2, 3 etc. See modes1.xls, a spreadsheet for calculating and plotting room modes and other room parameters discussed here. At frequencies below the lowest room resonance the sound pressure will increase at a rate of  12 dB/oct for a closed box speaker that is flat under anechoic conditions, assuming that the room is completely closed and its surfaces are rigid. This case has some significance for the interior of automobiles. Under the same circumstances the sound from a dipole speaker will stay flat. Domestic listening spaces are seldom completely closed, nor are sheet rock walls rigid, making a prediction of very low frequency in-room response extremely difficult. Note: Calculations of room modes, though popular, are not practical for predicting optimum speaker placement or listener position. For this one would need to calculate the transfer function between speaker and listener. The transfer function is related to the room modes, but much more difficult to determine. Never-the-less, room mode calculations ar e often invoked to predict "optimum" room dimensions. They fail to take into account any specifics about speaker  placement, source directivity and source type (monopole vs. dipole) that determine which modes are excited, and in combination with the absorption properties of different room surfaces, to which degree these resonances build up. Some people think that by making the room other  than rectangular or using curved surfaces, that they can eliminate standing waves. They merely change frequencies, shift their distribution and make their calculation a lot more difficult. Room modes can be identified by peaks and dips in the frequency response of the acoustic transfer function between speaker and listening position, though only at low frequencies ( xr  (13)

Example 3 Ls = 89 dB SPL at 1 W, 1 m Lref = 85 dB SPL Monopole: xr  = 1.04 m for T 60 = 300 ms Lr(1W) = 89 - 20 log(1.04) = 88.7 dB SPL Pref  = 85 - 88.7 = -3.7 dBW, equivalent to 10 (-3.7/10) = 0.4 W Dipole: xr  = 1.8 m for T 60 = 300 ms Lr(1W) = 89 - 20 log(1.8) = 83.9 dB SPL Pref  = 85 - 83.9 = 1.1 dBW, equivalent to 10 (1.1/10) = 1.3 W With a suggested 20 dB of SPL (= 100 x power) headroom over reference level the monopole requires 40 W and the dipole 130 W to set up a 105 dB SPL reverberant sound field. The dipole's direct sound, though, is 4.8 dB higher than the monopole's and will be 105 - 20 log(3/1.8) = 100.6 dB SPL at 3 m distance. The increased clarity could be traded off for a more lively room with larger T60 and the same 40 W amplifier power and direct-to-reverberant SPL ratio as for the monopole. C6 - Room response time It takes time to build up the reverberant sound field in a room. Combining the expressions for  rise time (2) and T 60 (3) we obtain Trise = 0.32 T60 [s] (14) You can think of Trise as the time constant of the room. If music or speech varies faster than the time constant, then the room will not respond fully and you hear predominantly the direct sound from the speaker. For 630 ms reverberation time and 200 ms rise time this covers modulation envelopes of a sound down to 1/200ms = 5 Hz which, in my opinion, is preferable over the 10 Hz envelope rate of a T 60 = 300 ms room. In all practical cases the room response time is large compared to the time it takes a reflected sound to reach the listener and therefore reflections will not be masked by the reverberant field. Depending upon the directivity of the source and the proximity of reflecting surfaces and objects specific absorptive or diffusive treatment may become necessary. It should not be overdone, though, because a certain amount of lateral reflection is subjectively desirable to not destroy the impression of a real space. Top

D - Loudspeaker and listener placement It is often assumed that a study of room acoustics can lead to highly specific loudspeaker and listener placement locations, down to within an inch. Other proponents are not as optimistic and recommend a 1/3rd rule (FAQ31). I have come to the conclusion that real rooms are acoustically far too complex to predict the transmission of sound from speaker to listener, where the sound paths are in three dimensions, have direction and frequency dependent attenuation and diffusion, and can excite the inherent resonance modes of a room to unknown degrees. From practical experience I recommend the following setups as starting points. They are for  ORION, a dipole or bi-directional loudspeaker, and for PLUTO, a monopole or omni-directional speaker. Three room sizes are considered. The 180 ft 2 (17 m2) room with 8 ft (2.4 m) ceiling would seem like the absolute minimum for quality sound reproduction with the ORION. A 400 ft 2 (37 m2) or larger room with 10' (3 m) ceiling should be perfect. D1 - Dipole setup ORION separation is 8'. They are slightly towed in. The listener is at the apex of an equilateral triangle. Distance to the wall behind the speakers is 4', and to the side walls 2'. The listener is only 4' from the wall behind, and this might require some heavy curtains and other absorbing material on that wall. As the room gets larger it expands around this triangular setup and especially behind the listener. Sound should just wash by the listener  and disappear. The wall behind the speakers should be diffusive. The rear  radiation from a dipole must not be absorbed or it is no longer a dipole. Similarly, the side walls should not absorb sound at the reflection points but diffuse it. A dipole can even be towed in so that the listener  sees the radiation null axis in a wall reflection mirror.

D2 - Monopole setup PLUTO setup differs from ORION. The listener sits closer  to the speakers. The distance to the wall behind the speakers can be slightly less, because of  the uniform acoustic illumination of the room. It should not be less than 3' (