PWL means sound power level, usually a dB comparison to 10^-12 Watts.
Of course +3 in PWL might be the same as +6 in SPL under the right circumstances.
David S.
If connected in parallel when the same voltage is applied across the drivers the electrical power will be +3dB, no ifs, ands of buts about it. Note- same voltage. SPL will may be spatially dependent. Assuming omni directional radiation for each source (talking about woofers here), in the frequency range where the drivers are correlated (long wave length compared to source separation) SPL will be uniform and both SPL and acoustic power will increase by 6dB for a 3dB increase in efficiency. At higher frequency, where the sources become uncorrelated, the SPL response will be spatially dependent and have a daizy pedal characteristic with peaks of +6dB separated by regions of nulls. In this region the radiated acoustic power will be + 3dB with no gain in efficiency. Between the two regions the transition will occur. The radiated power vs frequency will look like the center figure in the picture below with polar at selected frequencies to the right.
An externally hosted image should be here but it was not working when we last tested it.
Very good. One of the possibilities. I did a complete design/project for a member of diyAudio a long time ago.
PWL is the measure of acoustical power, essentially the nondirectional counterpart to SPL which is specific to a point in space. PWL can be calculated by measuring response over a sphere surrounding the object and integrating. It is more useful in acoustics (not electroacoustics) in that you can define the PWL of, say a truck, and define a distance and environment and calculate resultant SPL. Simply measuring the SPL of the truck wouldn't allow you to infer its SPL in another environment, you would need the PWL for that.
It relates to the 2 speaker question because the PWL change and the SPL change can be different. Two coherent sources will add to double the pressure or +6dB. This is a fact and is just the vector summing of pressure. For two woofers with equal path lengths to the microphone the SPL will go up 6dB over as wide a frequency range as you want to measure. By the same token, ground plane measurements give true frequency response +6dB. The real source and the virtual reflected source have equal path lengths for all frequencies because the microphone is on the ground.
For the power case we need to integrate all around any sphere surrounding the two units. (Interestingly we don't need the units centered in the sphere, the result is the same after integration.) If the units are less that 0.5 wavelength apart, then we will see a 6dB SPL gain in every direction and the power must have quadrupled. If the units are some wavelengths apart then we will see the nulls that you mentioned and, after integration, that the power has only doubled. This is from double the current/power being absorbed from the amplifier.
How can +6dB SPL equate to +6dB in PWL at low frequencies but only +3dB at high frequencies? At low frequencies the acoustic load has doubled and equivalent woofer efficiency is +3dB (and power absorbed accounts for the other 3dB). At high frequencies we haven't doubled the acoustic load but we have added 3dB to the directivity index. Both ranges equate to +6dB on axis.
David S.
It relates to the 2 speaker question because the PWL change and the SPL change can be different. Two coherent sources will add to double the pressure or +6dB. This is a fact and is just the vector summing of pressure. For two woofers with equal path lengths to the microphone the SPL will go up 6dB over as wide a frequency range as you want to measure. By the same token, ground plane measurements give true frequency response +6dB. The real source and the virtual reflected source have equal path lengths for all frequencies because the microphone is on the ground.
For the power case we need to integrate all around any sphere surrounding the two units. (Interestingly we don't need the units centered in the sphere, the result is the same after integration.) If the units are less that 0.5 wavelength apart, then we will see a 6dB SPL gain in every direction and the power must have quadrupled. If the units are some wavelengths apart then we will see the nulls that you mentioned and, after integration, that the power has only doubled. This is from double the current/power being absorbed from the amplifier.
How can +6dB SPL equate to +6dB in PWL at low frequencies but only +3dB at high frequencies? At low frequencies the acoustic load has doubled and equivalent woofer efficiency is +3dB (and power absorbed accounts for the other 3dB). At high frequencies we haven't doubled the acoustic load but we have added 3dB to the directivity index. Both ranges equate to +6dB on axis.
David S.
Very true. It took me a lot of pondering and head scratching some years ago to come to grips with it.
John K, I agree with your explanation. What are your 3 response cases, left to right?
David S.
First things first. The 6dB increase at low frequency has nothing to do with increased load. The radiation impedance seen by each driver remains the same. It is simply a matter of the fact that sound pressure is additive and in phase 1 + 1 =2. But SPL or intensity (watts/cm^2) and power response is a function of sound pressure squared. Thus, (1 + 1)^2 = 4.
The plots to the left and right are associated with power response when (left) there is no baffle step correction and right when there is a full 6dB baffle step correction. I took the figure to show the center plot which is correct for omni sources in free space but which was actually part of something else altogether.
But if I go from one woofer to two woofers and see 4 times the radiated power, what is the physical explanation? We know that half of that is really doubling the current and hence the power drawn from the amplifier. But the second doubling is a true doubling of efficiency with my two woofer system.
You need to explain why efficiency doubles.
David S.
Ok, so we are talking about low frequency here because we know that at higher frequency where the sources are uncorrelated there is no efficiency gain.
The power dissipated in each voice coil is I^2*Re, and with two VCs we have P = I1^2*Re + I2^2*Re and with I1 = I2 and the same Re, P = (I1^2 + I2^2)* Re = 2*I^2*Re. But with sound radiation it is different. Velocity is like current. The velocity field associated with the radiation of the first source is U1. The power is U1^2 * Zr where Zr is the radiation resistance. The power from the second source is U2^*Zr. But here the total power is not (U1^2 + U2^2) *Zr. The effective velocity due to both sources is the sum of the velocity from each, Ue = (U1 + U2), and the power is Ue^2*Zr = (U1 + U2)^2 * Zr, or with U1 = U2, (2U)^2 * Zr, = 4 U^2 * Zr. The velocity field generated by one source is simply added to that of the second source.
All the acoustic power is being dissipated into the same resistance, the acoustic resistance of air. In the VCs the power is being dissipated into the individual Re of each source. In the acoustic case is it like doubling the current through the single resistance of air.
3-Way MTM
If you search under "Dynavox LW6004PMR",
http://www.diyaudio.com/forums/multi-way/163796-some-design-help-please.html
It's a beautiful design of a 3-Way for a MTM (2 midwoofers+tweeter). The quality/specs of the two Dynavox was asking for this alignment and reinforcement (or attenuation) of the mid band that I think owner never tested/adjusted or concluded because he was looking for something else. But, he's design of the box (not the xover) is beautifully applicable and valuable for the beginning and lab simulation of this project.
Pranam, I found what you looking for.
If you search under "Dynavox LW6004PMR",
http://www.diyaudio.com/forums/multi-way/163796-some-design-help-please.html
It's a beautiful design of a 3-Way for a MTM (2 midwoofers+tweeter). The quality/specs of the two Dynavox was asking for this alignment and reinforcement (or attenuation) of the mid band that I think owner never tested/adjusted or concluded because he was looking for something else. But, he's design of the box (not the xover) is beautifully applicable and valuable for the beginning and lab simulation of this project.
Ran across this on the web. It seems to better explain the +3, +6 question.
Mutual Radiation Impedance
By Bohdan Raczynski
When two loudspeakers are mounted on the same baffle and fed the same signal, one driver starts to produce additional pressure on the other, increasing its radiation impedance. The next logical step is therefore to determine power radiated by two sources mounted on the same baffle. Vanderkooy and Lipshitz [3] examined a simple case of two pistons mounted in an infinite baffle and proposed an elegant formula for expressing radiated power into the farfield taking into account self and mutual radiation impedance of source1 (piston1) coming from itself and from piston 2.
For low frequencies, the above result is four times (or 6dB SPL) the single source result. Factor k, plotted for single driver vs. frequency (Figure 4) exhibits 3dB raise at low end of the spectrum and 0dB at the high end of the frequency range. For two drivers, the curve is up by 3dB and it can be observed, that 3dB gain in SPL is attributed to doubling the electrical power supplied to two drivers connected in parallel. Additional 3dB gain in SPL is due to mutual radiation impedance effect. Engebretson in [4] indicated, that this additional increase in effciency will hold to a frequency above which the diaphragms no longer "couple". This phenomenon has been experimentally verified by Gander and Eargle in [5]. They have performed comparative measurements on single subwoofer loudspeaker vs. an array of 8 subwoofers noting increase in SPL at 30Hz as 21dB. Of this gain, they attributed 9dB to 8-fold increase in input power (8 = 2x2x2 = 3dB+3dB+3dB) and 9dB to mutual coupling increasing 3dB per doubling of units. Additional 3dB gain was due to slight increase in directivity index of this large array. Also, Keele [6], investigating the performance of Bessel Arrays concluded that an array of two loudspeakers simply connected in-parallel, exhibits maximum SPL increase of 6dB, but only up to a frequency where the sources are about 1/4 wavelength apart.
Mutual Radiation Impedance
By Bohdan Raczynski
When two loudspeakers are mounted on the same baffle and fed the same signal, one driver starts to produce additional pressure on the other, increasing its radiation impedance. The next logical step is therefore to determine power radiated by two sources mounted on the same baffle. Vanderkooy and Lipshitz [3] examined a simple case of two pistons mounted in an infinite baffle and proposed an elegant formula for expressing radiated power into the farfield taking into account self and mutual radiation impedance of source1 (piston1) coming from itself and from piston 2.
For low frequencies, the above result is four times (or 6dB SPL) the single source result. Factor k, plotted for single driver vs. frequency (Figure 4) exhibits 3dB raise at low end of the spectrum and 0dB at the high end of the frequency range. For two drivers, the curve is up by 3dB and it can be observed, that 3dB gain in SPL is attributed to doubling the electrical power supplied to two drivers connected in parallel. Additional 3dB gain in SPL is due to mutual radiation impedance effect. Engebretson in [4] indicated, that this additional increase in effciency will hold to a frequency above which the diaphragms no longer "couple". This phenomenon has been experimentally verified by Gander and Eargle in [5]. They have performed comparative measurements on single subwoofer loudspeaker vs. an array of 8 subwoofers noting increase in SPL at 30Hz as 21dB. Of this gain, they attributed 9dB to 8-fold increase in input power (8 = 2x2x2 = 3dB+3dB+3dB) and 9dB to mutual coupling increasing 3dB per doubling of units. Additional 3dB gain was due to slight increase in directivity index of this large array. Also, Keele [6], investigating the performance of Bessel Arrays concluded that an array of two loudspeakers simply connected in-parallel, exhibits maximum SPL increase of 6dB, but only up to a frequency where the sources are about 1/4 wavelength apart.
since its going to be a bi-amped system, can i safely take the value of nominal impedance of 8 ohms which when connected in parallel gives 4 ohms as the total impedance presented to the amplifier? because while designing passive crossovers we hardly consider nominal impedance in our calculations.
will the amp rated at 4 ohms be able to handle a load which is slightly below 4 ohms in the worst case?
will the amp rated at 4 ohms be able to handle a load which is slightly below 4 ohms in the worst case?
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