It is not uncommon to find manufacturer specifications that make you wonder. Especially in the case of power and sound pressure specifications, strange combinations are often encountered. It is relatively easy to determine whether, for example, a loudspeaker equipped with two 20cm drivers really produces the sound pressure that marketing department would like it to…
Diaphragm area and stroke
The maximum sound pressure is limited, especially in the low frequency range, by the linear stroke and the area of the woofer’s diaphragm. The more surface area and stroke (or the resulting displacement volume) there is, the more sound pressure can be achieved. The radiated frequency plays a key role here. To achieve the same sound pressure at half the frequency, four times the stroke or four times the area is required.
115 dB SPL at 15 Hz?
As an example, one manufacturer specifies a lower cutoff frequency of 15 Hz and a maximum sound pressure of 115 dB at the same time. What to think of having two woofers of about 20cm? We can easily calculate this with the following equation: Lp = 20log(a x f² x Vd), where a is a constant with the value 0.37 and Vd is the displaced volume. Let’s assume the radius of the diaphragm is 8.5 cm and the maximum stroke +/- 10 mm, which is a very good value.
The picture beside shows the calculated maximum sound pressure of one (red) or two 20cm woofers (blue, + 6 dB) with a maximum excursion of +/- 10mm. At 15 Hz, 88 dB are reached, the promised 115 dB are only achieved at around 70 Hz. It does not matter what kind of bass driver it is. What matters is the stroke and the area of the diaphragm(s).
Due to digital technology it is possible to couple the lower cutoff frequency to the level. This means that at higher levels the lower cutoff frequency is increased. While at 85 dB, for example, the lower cutoff frequency is at the effectively promised 15 Hz, this is shifted to 20 Hz at 90 dB, to 30 Hz at 100 dB and up to 115 dB at 70 Hz. If this happens on a small scale, as is common today with small Bluetooth- and multi-room speakers, it remains almost inaudible and the woofer is not mechanically overloaded. The disadvantage of such a control is, of course, that music with a lot of low bass is still limited in level and thus represents a compromise for high-quality music reproduction. Unfortunately, nothing can replace diaphragm stroke and area. The disadvantage is that woofers that can perform a large linear excursion and at the same time are low in distortion are very rare and can only be found in higher price regions.
115 db and 15 Hz lower cutoff frequency are possible, but not at the same time. As always with such statements, they can be justified in one way. To be fair, it would of course have to be specified at which frequency the 115 dB is reached or what maximum level is possible at the 15 Hz. In a listening room, higher levels can usually be achieved at certain frequencies because the room can amplify sound in the low frequency range through various effects.