Subwoofer Sensitivity

[Impious 1,476]

What is sensitivity? The sensitivity of a driver is typically defined as the sound pressure level of the loudspeaker given 1 watt of power input, measured at a distance of 1 meter, measured on-axis with the loudspeaker and measured in infinite space with the loudspeaker mounted to an infinite baffle. While the later part is typically assumed but not stated, the former part is the reason you generally see “1w/1m” or “2.83V/1m” stated along with the sensitivity specification.

But wait, is 1w/1m equal to 2.83V/1m? The answer is only for an 8ohm impedance driver. We know this because of ohms law, where Power = Voltage^2/Resistance. If the load is anything other than 8ohm then the resulting sensitivity rating will not be a 1w measurement! If the driver is 4ohm and the measurement is a 2.83V measurement, we can find the amount of power input with the formula 2.83^2/4 = 2w. This means that sensitivity will be overstated by 3db compared to a true 1w measurement. I have seen many unscrupulous companies take a dual 2ohm/coil subwoofer, wire the coils in parallel and then rate sensitivity at 2.83V, overstating sensitivity by 9db!

Due to these and other variations in rating methods and some manufacturers not even stating a method, it can often be difficult to directly compare one subwoofer’s sensitivity to another’s. However, if you are able to obtain the Thiele-Small parameters for the subwoofer there is one surefire way to calculate an accurate sensitivity measurement for a driver. And that is with the following formulas;

Efficiency (N₀) = 9.64 * 10^(-10) * Fs^3 * Vas / Qes

*To express as a percent, multiply by 100

*Vas in liters

Sensitivity (SPL) = 112 + 10*Log(N₀)

The Efficiency (N₀) calculation expresses, typically as a percentage, the amount of power input that is converted to acoustic power. With the sensitivity calculation we can convert the efficiency of the driver to a 1w/1m sensitivity rating. As long as the T/S parameters are accurate, utilizing this formula will put any two drivers on a level playing field and allow you to directly and accurately compare sensitivity (or efficiency) between drivers.

Okay, but higher is still better because higher means it’s louder, right? Not necessarily the case. There are a few issues here that need to be discussed to better understand why.

From a driver design perspective, we can see from the above formulas that there are two ways in which to increase sensitivity for a given driver diameter; increasing Fs or decreasing Qes (or both). Adjusting either of these two parameters, however, is ultimately going to affect how the driver responds in a given enclosure. And this relationship, as it relates to enclosure size, sensitivity and low frequency extension, has been defined through a rule known as Hoffman’s Iron Law. As you can see from the link (which I highly suggest you read), it’s already been covered in relative detail elsewhere on the site. But it’s important to us here, so it’s worth touching on again.

In short, Hoffmans Iron Law states that we can only have two of the following three;

• Low frequency extension
• Small enclosure
• High sensitivity

What’s important to take away from this is that if you want high sensitivity and a small enclosure, you will necessarily sacrifice low frequency extension. Or, conversely, if you desire extended low frequency output from a small enclosure, you must necessarily sacrifice sensitivity. While a given driver may have a higher rated sensitivity, that driver may actually have less output in the subbass region once the effects of the enclosure are taken into consideration since it may begin it’s rolloff at a higher frequency. And given in car audio we typically require reasonable enclosure volumes, having a high sensitivity can actually be disadvantageous.

The second factor we need to consider is how output is achieved. Sensitivity isn’t what determines maximum output. Output is a function of air displacement. The maximum amount of linear displacement (Vd) you can achieve is limited by your cone area (Sd) and linear excursion (Xmax). As you increase the amount of displacement at your disposal, you increase the potential linear output you can achieve. Even though a driver may have a higher sensitivity, if it’s maximum linear displacement (Vd) is less than that of a driver with a lower sensitivity, the lower sensitivity driver will have the potential for higher levels of output.

We also have to consider the effects of Power Compression (and I again urge you to read the link). Consider the effects of power compression applied to our scenario. A higher sensitivity driver may, for example, begin to experience more power compression at a lower output level than a lower sensitivity driver. If this is the case, then as output is increased beyond that level the higher sensitivity driver would gain less output for each increase in power and experience more parameter shift.

The basic summary is that after many factors are taken into consideration, it is impossible to state unilaterally that higher sensitivity drivers will better than lower sensitivity drivers. Generally choosing one driver over another based on sensitivity alone is a bad path to follow. Sensitivity is just one of a multitude of parameters that all conspire together to define the performance of a loudspeaker. And in my humble opinion, it is one of the less important factors to consider. As with anything, there are compromises to be made and it's necessary to find the best set of compromises for your particular situation.

[jrod1050 5]

Very well put. Quality read right here

[Aaron Clinton 2,372]

Thank you for the write up Brad!

[j-roadtatts 1,129]

thank you for spewing your knowledge on us.

[jcarter1885 995]

, read at least two times already.

[Notorious97200 339]

Thanks for these info.

Gotta read these links asap.

[Don Ganso 13]

Who are you? What are you? What made you so smart?

Quality read!!!

[Duran 387]

Who are you? What are you? What made you so smart?

Quality read!!!

Behold the all-knowing audio robot known only as 'Brad'

Good read man

[ryan s 12]

On this subject...I was once reading an Alpine manual to help a friend with his Type E subs. There was an asterisk next to the sensitivity number. Hmm. Measured at 1W/1M...what's the asterisk for?

Scroll down, and a blurb reads...well, read it for yourself. Page 3 http://vault.alpine-usa.com/products/documents/OM_SWE-1243.PDF

It's not "the output number," true, but rather a spec one should know and be familiar with.

This is a great thread

[Impious 1,476]

On this subject...I was once reading an Alpine manual to help a friend with his Type E subs. There was an asterisk next to the sensitivity number. Hmm. Measured at 1W/1M...what's the asterisk for?

Scroll down, and a blurb reads...well, read it for yourself. Page 3 http://vault.alpine-...OM_SWE-1243.PDF

LOL....always nice to see manufacturers combating ignorance, even if it's just a brief footnote!

Glad you guys find this thread useful

[SaxMan 2]

What. Is your. Profession? Seriously I want to possibley enter the same field of work...

[Impious 1,476]

What. Is your. Profession? Seriously I want to possibley enter the same field of work...

This is just a hobby My "day job" is wholly unrelated.

[ssh 924]

What. Is your. Profession? Seriously I want to possibley enter the same field of work...

This is just a hobby My "day job" is wholly unrelated.

His day job is juggling, I thought everyone knew that...