Tutorial: SPL Calculator on PAcalculate app

Tutorial: SPL Calculator on PAcalculate app


Hello, this is Joe Brusi developer of ‘PAcalculate’, the free multi-platform app for mobile phones and tablets with calculators, reference information such as pinouts, like this useful speakON NL8 drawing, as well as utilities such as an inclinometer, or a flashlight, or a light screen for theater applications. As far as calculators go all of them include relately lengthy help text here at the bottom of the screen, or if we had a mobile phone with a smaller screen, that text screen would be accessed through an info button like this. So that help information is integrated within the app but in this first video tutorial we wanted to complete this information with more detailed explanations on the sound pressure level related calculators. The SPL calculator calculates a resulting total direct sound SPL. As well as doing that it provides partial results that you can see here on the right hand side with the yellow background. On smaller screens these corrections you’ll find them here at the bottom of the resulting SPL. The calculation is for parameters that you see on the screen: sensitivity, power, number of speakers with phase, and distance, so that means other factors such as air attenuation, reverberation, wind, or pressure gradients that could curve the sound upwards are not considered. Also not considered is the loss of sensitivity due to loudspeaker heating or the signal crest factor, which means that, depending on the amplifiers peak power output, we will have more SPL for a modern song with little dynamics than for an uncompressed live sound audio or songs from the 70s or 80s that were recorded with much more dynamics than those of today. The first input field is sensitivity, which is the sound pressure level produced referenced to a distance of 1 meter with an input of 1 watt. Of course, with sensitivity, the higher the better because that means we have more pressure for the same amount of input power. Here we would enter the nominal sensitivity from the manufacturer’s spec sheet but you should know that sensitivities are not all born the same and manufactures could use different criteria that could result in slightly different results, say plus minus 2 dB, This sensitivity data that we introduced here is the base SPL to which corrections of power, number of speakers, and distance are added, to get a total resulting SPL. Next field is the power that an amplified channel delivers to each loudspeaker enclosure if we have a box with more than one speaker then we will treat it as a black box (because we don’t care what’s inside) and we’ll use the number of boxes in the number of loudspeakers field and in the sensitivity field we’ll use the sensitivity of the entire box. If we have several boxes connected to the same amplifier channel then we’ll enter the power of the amplifier channel divided by the number of boxes. For example if we have 2 boxes of 8 ohms each connected in parallel and the amplifier delivers a power of a thousand watts into a 4 ohm load then we’ll enter a power level of 500 watts. It’s important here to enter real power based on RMS voltage. These days a lot of manufacturers use peak power which is twice as much or specifications based on sinewave busrts, and that’s a power that cannot be maintained continuously. Of course doubling the power means adding 3 dB to the SPL so when we go from 500 watts to 1000 watts we go from 27 to 30 dB. Next is the number of boxes that we enter the sensitivity for in the first field of the calculator. As we could expect doubling the number of in-phase loudspeakers gets us an increase of 6 dB in SPL, we double again we have an extra 6 dB,if we double again to 8 we have a final total correction of 18 dB for 3 times doubling of the number of speakers (from 1 to 2 to 4 and to 8) whereas if we switch to the random phase option, then it becomes 3 dB per doubling, There a total of 9 dB for 8 speakers carrying independent signals. If we had 2 loudspeakers, one on each side, carrying totally different signals, such as instruments and voices that had been panned completely to the right or to the left, the sum of the sound pressure level from each speaker would be 3 dB more and that would happen pretty much anywhere within a room. However if we have the same two speakers carrying the same signal, the only points in space were the contributions from the two speakers arrive at the same time is this center line here, so only points along this line would get a total summation with no interference. therefore 6 dB extra decibels. However for any other positions outside of this center line the time arrivals from the sources would be different and that would mean the possibility of interference Depending on the frequency and the time arrival difference we might get total summation, if we’re lucky, 6 dB more. Total cancellation if we are unlucky or somewhere in between, that’s why as a way to make some kind of an average throughout the area we tend to use the random phase option in the SPL calculator, so that we have an average result which is also a conservative result, so if there is any additional gains because because of the spacings at loudspeaker or the size of the room then that’s something that will will add to our conservative estimate; we’d rather have a more realistic conservative estimate than overestimate the result. On the other hand if we had an array of subwoofers in the center, then pretty much anywhere in the room time arrivals are similar and considering that low frequencies have very large wavelengths In this case we could more or less use the in-phase option for the SPL calculation with relative certainty. As the last field we have the change of SPL contributed by distance to the source. That works with the inverse square law, so, of course, when we double the distance (which we can enter in meters or feet) we decrease 6 dB. If we double again we have again 6 dB less; if we double again we have a total of -18 dB. If we want to calculate the effects of air absorption for a specific frequency we can use the air absorption calculator here we can see the effect of different variables in the total attenuation. For instance, temperature does have an effect, but if you watch the result field here at the bottom it’s not a great difference. Let’s go back to 25 degrees (again we can use Celsius or Fahrenheit here) As far as the relative, humidity water is a much better conductor of sound than air is, so that means the humidity has a big impact: for instance here we have a relative humidity of 15% with 3.5 dB loss. If we go to 50% humidity then that’ll go down to 1,3. Distance is also, of course, key. If we change this 15 to, say, 100, that increases dramatically. And frequency is also key: if we change this 8,000 Hertz to 16,000 we would in this case almost quadruple the air loss attenuation. The last sound pressure level related calculator is SPL addition, that allows us to add multiple SPLs with a phase option that should be used in the same way we saw before. Here we can see for instance that if we have two dB SPLs spaced by 10 dB, if the phase option is at ‘random phase’ then the end result is pretty much the largest SPL we had to begin with, whereas if we switch to ‘in phase’ now it’s relatively significant. As a final note, it’s really important to put the meaning of dB into perspective and to remember what level changes in dB mean: a change of 10 dB is perceived as a change of doubling the loudness, whereas 3 dB are basically just a noticeable change and 1 dB would hardly be noticeable at all, especially when playing music. That’s all for now. See you next time!

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