# Microphone in box low frequency measurement technique -help required!

#### Razorhelm

##### Active Member
I found the following method for measuring the low frequency output of a speaker.

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” (&#x221d 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.

#### bigjacko

##### Addicted to Fun and Learning
So are you trying to know the exact spl of the speaker?

Some experts like to use this method too. I forgot where is the best point to do measurement, close to wall or right in middle of box.

OP

#### Razorhelm

##### Active Member
the key for me is the shape of of the frequency response for eq-ing

I want to get the speaker output flat via a dsp amp which is running it.

from what i have read you want the microphone to be in the middle of the enclosure

#### bigjacko

##### Addicted to Fun and Learning
If only interested in frequency response we can forget about the equations for now.

In the middle of box is not that easy to reach for closed box or passive radiator. Maybe DIY a small capsule and put in there?

#### mwmkravchenko

##### Active Member
Why don't you do a nearfield spl response? If your enclosure is sealed you will have the response all clean and tidy. If you have a port you will also need to do a port mesurement and then splice the results. REW can do this, so can Vituix. Don't know if CLIO has this function.

Mark

#### bigjacko

##### Addicted to Fun and Learning
Why don't you do a nearfield spl response? If your enclosure is sealed you will have the response all clean and tidy. If you have a port you will also need to do a port mesurement and then splice the results. REW can do this, so can Vituix. Don't know if CLIO has this function.

Mark
I found some variations when I do near field plus splice compare to ground plane. Too much small details that needs to be taken care. 1mm difference can probably throw response 1dB off. I don't even know the exact time difference between passive radiator and woofer, I normally just align until there is a deep null.

Another problem that can't be solved by amateur like us is account for different shape of woofer cone. I tested Purifi aluminum and PP cone. For near field aluminum one has like 3dB lower sensitivity. For ground plane it showed 1dB difference which is correct.

Having a way that is robust is more ideal. Ground plane is pretty good but need a lot of space.

#### mwmkravchenko

##### Active Member
I found some variations when I do near field plus splice compare to ground plane. Too much small details that needs to be taken care. 1mm difference can probably throw response 1dB off. I don't even know the exact time difference between passive radiator and woofer, I normally just align until there is a deep null.

Another problem that can't be solved by amateur like us is account for different shape of woofer cone. I tested Purifi aluminum and PP cone. For near field aluminum one has like 3dB lower sensitivity. For ground plane it showed 1dB difference which is correct.

Having a way that is robust is more ideal. Ground plane is pretty good but need a lot of space.
What you are fretting over is so swamped by room placement, your position in the room that it is chasing the end of the rainbow. Keep to what you have done. Ground plane is really only of use for the last 2 octaves 16 to 32 hertz and 32 to 64 hertz. Conventional wood framed homes are basically invisible to bass below about 30 hertz. If you want accurate SPL and ultimate SPL from your enclosure then do a groundplane measurement. Otherwise a close mic is more than adequate.

I suffer from OCD to. And have learned over decades to turn in down when it is not needed.

Mark

OP

#### Razorhelm

##### Active Member
I did have some success with this, however I have not had time to post the results.

I lowered the mic in via the port, so I will have a slight error due to the port being very slightly reduced by the mic cable.

But it gave a new clean curve once transformed by the equation.

I used it to eq the output to flat from 40hz - 200hz and it measured well as part of a 2.2 speaker setup so I think it works pretty well.

I'm in a flat in London so very little space to work with, so this method seems the best compromise.

OP

#### Razorhelm

##### Active Member

This is the corrected response I obtained and it matched what I was expecting to see, considering enclosure size and driver.

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