#### Razorhelm

##### Active Member

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https://www.audiomatica.com/wp/wp-c...Loudspeakers-at-low-Frequencies-with-CLIO.pdf

https://audioxpress.com/article/measuring-loudspeaker-low-frequency-response

I'm getting lost at this stage of the audio express article:

To determine the low-frequency response of the two-way example, only one measurement of pressure inside the enclosure is needed! Not only that, but because there is only one measurement, phase information is not required. The governing equation can be written as follows:

pR = kf2pB [7]

pR is the pressure at a distance outside the enclosure. pB is the pressure inside the enclosure. k is a constant. f is the frequency in hertz.

Equation 7 is not too useful in its present form. The squaring operation will lead to rather large numbers. This can be avoided by normalizing the equation to the starting frequency, f0. Furthermore, the result should be in decibels. So, first rewrite Equation 7 like this:

pR = k (f / f0)2 pB [8]

k is now a different constant. Now, take the logarithm of both sides and multiply by 20 to convert Equation 8 into an equation in decibels:

20 log (pR) = 20 log (k) + 40 log (f/f0) + 20 log (pB)

or:

pR (dB) oc 40 log (f/f0) + pB (dB) [10]

The symbol “oc” (∝ can be read as “proportional to.” Recall that the logarithm of a squared quantity is just twice the logarithm of the quantity itself. Now, the large number squaring has been avoided.

I think the formula is not rendering correctly and i'm struggling to figure out what it was

I think the last line should be

pR (dB) "is proportional to" 40 log (f/f0) + pB (dB)

but I am not sure.

I think you then plot "40 log (f/f0) + pB (dB)" where pB(dB) is your measurement and this gives you your low frequency output curve.

Original referenced paper

https://www.renatogiussani.it/pdf/Simplified-Loudspeaker-Measurements-at-Low-Frequencies.pdf

my speaker is 3d printed so easy to add a measurement hole - and the driver is flipped so more tricky than usual to work out cone radiating area, thought this could be a better method for this design than the usual nearfield sum.