equation for internal pressure in ported enclosure

[batdorf9]

Is anyone aware of an equation for calculating the internal box pressure in a ported enclosure? This seems pretty straight forward for a sealed enclosure, but much more complicated for a ported enclosure. I've googled and searched here, and I have not found anything. Thanks!

-Robert

[kelticwizard]

I don't know if the equation for internal pressure is calculated, but the Thiele-Small closed and vented box articles are here:

http://www.readresearch.co.uk/HTML/articles.htm

[noah katz]

I know of no such equation, but it should be close to what the pressure is in sealed box that's outputting the same dB at the same freq.

[Svante]

The sound pressure level (SPL) inside the box is

20*log10( (4*r*pi*c²)/(w²*V) )

...decibels higher than the SPL at the distance r, if the speaker is placed in free space, and the box dimensions are much smaller than the wavelength. c=345 m/s, V=box volume, w=2*pi*f, f=frequency.

The baffle step is neglected.

In fact this is the basis for a rather clever method of determining the anechoic response of subwoofers; put the microphone inside the box, tilt the response by 12 dB/oct (due to the quadratic relation to the frequency) and voilá: there is the response outside the box. No need for expensive anechoic chambers, and no more measurements in the back yard.

Note: doing the math usually results in a 40-60 dB boost at low frequencies, in other words if the system plays at 100 dB at 1 metre, the leven inside the box is 140-160 dB. This seems unreasonably loud, but is true for many systems. This in turn leads to that measuring the response with the mic inside the box very easily leads to overloading of the microphone, which may seem very counterintuitive since the sound outside the box is not very loud.

The equation is identical for both closed boxes and bass-reflex.