Sensitivity and Decibels: The Maths That Matters
Sensitivity and decibels together tell you how loud a driver gets and what each extra watt buys. Because power maps to level as 10·log₁₀, doubling amplifier power gives only 3 dB, while 3 dB of extra sensitivity does the same job for free. Know the handful of rules below and you can compare drivers and plan a rig on paper.
What the sensitivity figure means
Sensitivity is SPL at 1 m on axis for 1 W input, or for 2.83 V, which is 1 W into 8 Ω. Read the conditions before comparing:
- 1 W vs 2.83 V: 2.83 V into a 4 Ω driver is 2 W, which reads 3 dB higher than the 1 W figure.
- Half space vs full space: a driver measured in a baffle on a large boundary (half space) reads up to 6 dB higher at low frequencies than the same driver in free space.
- Averaging band: a figure averaged over a narrow, favourable band reads higher than one averaged over the driver's full working range.
The rules
| Change | Effect on level |
|---|---|
| Double the amplifier power | +3 dB |
| Ten times the power | +10 dB, roughly perceived as twice as loud |
| Double the voltage | +6 dB (four times the power) |
| Double the distance, point source in free field | −6 dB |
| Second identical sub alongside, same signal | Up to +6 dB at low frequencies |
| Driver 3 dB more sensitive | Same level from half the power |
Why subs stack
At 50 Hz the wavelength is 343 / 50 = 6.9 m. Boxes spaced well inside a wavelength add in phase and behave as one source. Two subs on two amp channels give +3 dB from double the input power and +3 dB from coherent summing: +6 dB in all. Four give +12 dB. That is the case for building a wall of bins rather than chasing a bigger amp. The real counts are in how many subs.
From sensitivity to maximum level
Theoretical maximum at 1 m = sensitivity + 10·log₁₀(rated power). For the WM1850/8, rated 93.5 dB at 1 W:
- At 1800 W AES: 93.5 + 32.6 = 126.1 dB.
- At 3600 W peak: 93.5 + 35.6 = 129.1 dB.
These are ceilings for a single driver in the sensitivity measurement conditions. Power compression takes some of it off as the coil heats; box loading, boundaries and stacking add to it. The calculation is still the right way to compare drivers: sensitivity and power handling count together. A driver 3 dB less sensitive needs twice the power to match, so power handling is worth only as much as the amp behind it.
Power for the money
The WM1850/8 is £275 for 1800 W AES (15.3p per rated watt); the WM18X451 is £345 for 1800 W RMS (19.2p per rated watt). Rating standards differ between makers, so compare the method as well as the number: see power ratings explained.
Sources: decibel relationships are standard (L. L. Beranek, Acoustics). Speed of sound 343 m/s at 20 °C. Wavemark WM1850/8 spec sheet and WM18X451 product data. Calculated values rounded.
Questions
How much louder is double the amplifier power?
3 dB. Level in dB is 10 × log10 of the power ratio, so doubling power adds 3 dB and ten times the power adds 10 dB.
Is 2.83 V sensitivity the same as 1 W sensitivity?
Only for an 8 ohm driver. 2.83 V into 4 ohms is 2 W, so a 4 ohm driver's 2.83 V figure reads 3 dB higher than its 1 W figure.
How much louder are two subs than one?
Up to 6 dB when they sit close together on the same signal: 3 dB from double the power and 3 dB from the outputs summing in phase at low frequencies.
How loud can an 18 inch sub driver go?
Add 10 × log10 of the power rating to the 1 W sensitivity. The WM1850/8 at 93.5 dB and 1800 W AES gives about 126 dB at 1 m, before power compression and before any gain from the box or stacking.