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Props to Grand Masta @ sounddomain.com



For everyone wanting to predict "Cabin Gain" (their vehicles transfer function)
by Josh Sanders

Assuming we have a perfect sound source.

(1) Treating the car as a small, empty, rigid, air tight, closed, box without standing wave resonances

This will give you a 12dB/oct raise in low frequency when the sound starts to act in pressure mode rather than wave mode. This is at frequencys below the lowest room resonance. Frequency of lowest room resonance = ( speed of sound / ( 2 x longest length in the enclosure))

(2) Treating the car as a small, empty, rigid, LEAKY, closed, box without standing wave resonances

The SPL gain in (1) will be attenuated as the pressure will not be directly proportional to the sound source.

(3) Treating the car as a small, IRREGULARLY STUFFED AND LINED , rigid, LEAKY, closed, box without standing wave resonances

Same as (2), but now the higher frequencys will be attenuated more than the lower frequencys.

(4) Treating the car as a small, IRREGULARLY STUFFED AND LINED, rigid, LEAKY, VENTED, box without standing wave resonances

Above the vent frequency the losses in (2) are reduced. At the vent frequency there is gain and below the tuned frequency there is severe attenuation. This effect is reduced because the vent has a large resistance, and the enclosure is leaky. With all of the windows up and doors shut, the tuned frequency will be infrasonic. (3) effect this the same as it effected (2) so The response is similar to (1) with infrasonic frequencys severely attenuated and the gain no longer approaches infinity at DC. With a window wound down or a door open ajar, the tuned frequency moves up into the audiable spectrum. The result is a noticeable gain at the tuned frequency and severe attenuation below the tuned frequency.

(5) Treating the car as a small, IRREGULARLY STUFFED AND LINED, rigid, LEAKY, VENTED, IRREGULARLY SHAPED ENCLOSURE

Similar to (4) but now at different locations inside the car there will be different gain/attenuation at ¼ wave frequencies. This effect is reduced by the irregular shaped enclosure, irregular stuffing inside the enclosure, and lining on the enclosure walls. If the frequency is such that the enclosure is acting in pure pressure mode as stated in (1) then there are no standing waves below the frequency of lowest room resonance.
The response of standing waves in a car is beyond the scope of this article and therefore will not be predicted.

(6) Treating the car as a small, IRREGULARLY STUFFED AND LINED, SEMI-RIGID, LEAKY, VENTED, IRREGULARLY SHAPED ENCLOSURE

Similar to (4) for small signal simulation. For large signal there is gain when the enclosure walls resonate out of phase with the sound source, and attenuation when the enclosure walls resonate in phase with the sound source. The amount of gain/attenuation is incresed as SPL inside the car increases.

Conclusion

Small signal prediction of car with windows up:

An inverted hipass with
f = Frequency of lowest room resonance = ( speed of sound / ( 2 x longest length in the enclosure))
Q = 0.707
Order = 2 = 12 [db/Oct]
infra sonic frequencys will not accurate

With WinISD 0.50a7
infra sonic frequencys will not accurate but better than above.

internal car length = l [m]
Linkwitz transform
f0 = c / 2l
fp =15
Q0 =0.707
Qp =0.707

Eg
internal car length = 1.9m
Linkwitz transform
f0 =90
fp =15
Q0 =0.707
Qp =0.707

internal car length = 2.2m
Linkwitz transform
f0 =80
fp =15
Q0 =0.707
Qp =0.707

internal car length = 2.5m
Linkwitz transform
f0 =70
fp =15
Q0 =0.707
Qp =0.707

internal car length = 2.9m
Linkwitz transform
f0 =60
fp =15
Q0 =0.707
Qp =0.707

internal car length = 3.5m
Linkwitz transform
f0 =50
fp =15
Q0 =0.707
Qp =0.707

Refrence: Seigfried Linkwitz
http://www.linkwitzlab.com/images/graphics/enclosure-spl.gif

WARNING

The Following graphs are incorrect when using a Linkwitz transform to predict "Cabin Gain"
Transfer function phase
Group Delay
Maximum SPL
Amplifier apparent load power
Cone excursion
Passive radiator - all
Port air velocity
 
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