Car Cabin Gain Estimator
Model how a vehicle's cabin boosts low frequencies by 12 dB/octave and how that combines with your sealed subwoofer.
Inputs
Sub-to-rear-of-cabin acoustic length, including trunk if open to cabin.
Lower = tighter car = more gain survives to the bottom. Typical: 8–20 Hz.
How it works
Inside a small closed space like a car, a wave much longer than the cabin cannot form a standing wave, the whole cabin simply gets compressed and decompressed like a pressure chamber. As frequency drops below the cabin’s transition frequency, the output measured at the seats rises at 12 dB per octave. That boost is called cabin gain.
f_T ≈ c / (2·L_cabin) Gain(f) = 10·log₁₀( (1 + (f_T/f)⁴) / (1 + (f_L/f)⁴) ) Total = Subwoofer response + Gain
The second term models leakage (windows, doors, the sunroof) which lets pressure escape at very low frequencies, so the gain flattens out and eventually falls again below the leakage corner f_L. A tight, well-sealed car (low leak frequency) can produce 12 dB or more of gain at 25–30 Hz.
This is why subwoofers measured in a lab (anechoic) and in a car sound completely different, and why many car installers choose a smaller sealed box with a higher Qtc, the cabin supplies the deep bass the box gives up. Ported boxes tuned too low (for example 25 Hz) can sound weak or “boomy” in a car because the cabin already boosts those frequencies. Treat the result as an illustrative model: real vehicles vary widely with size, openness and seat positions.