In my previous article, I made a case in favour of using subwoofers in a music system to achieve a more accurate bass response. Now in this article I address a common objection to the idea. Here we will discuss a popular myth from an objective point of view.

Fast bass

In this article we explore one aspect of the subjective term “fast bass.” The problem with this term starts when it is used to refer to anything beyond a subjective description of bass. As long as we use it to describe bass that sounds tight, controlled and accurate, we have no problem, except that people tend to use that term to describe subjective experiences that are not the same. Confusion comes in where the subjective term gets mixed up with mass, acceleration and velocity. The myth we will investigate here is that heavier cones take longer to respond to an impulse. I’ve set up an experiment that demonstrates how we can alter the time a woofer takes to respond to a transient impulse. We will soon see that mass has no effect at all.

Choosing the right analogy

A car analogy is often used. We all know a sports car with a light body and a powerful engine accelerates faster than a heavy bus. In reality this is a misleading analogy that merely serves to misrepresent what really happens. A better analogy is one in which both vehicles go over a speed bump whilst driving side by side at 60 km/h. Both are travelling at the same speed. The much greater mass of the bus means that more energy is required to move it. In speaker terms, a lighter woofer will be more efficient and require less power for the same output. Here, input power is analogous to fuel consumption. Both vehicles, regardless of their mass will go over the bump at the same time. In the same way, the time it takes for a woofer to respond to a transient signal is not affected by the mass of the cone.

In order to demonstrate what really happens, I set up an experiment to test the impulse response of a low mass woofer and how it responds to added mass. The focus of this experiment is to investigate the rise time of the impulse.

The woofer

The chosen woofer is a low mass pro audio driver. It is a 12” bass driver and the mms (moving mass) is low in order to achieve high sensitivity. The woofer is Eminence Delta 12.

Fig 1 – Eminence Delta 12 woofer used for the test.

The impulse response was measured near-field, with the mic close to the cone in order to exclude room effects in the measurement. During this experiment, care was taken to ensure that neither the mic or woofer moved. The mic was placed very close to the cone so that the direct sound swamps room effects.

Fig 2 – Near-field frequency response. The smooth response below 400 Hz indicates the absence of room effects due to the near field measurement technique.

Fig 3 – Near-field waterfall plot. The smooth decay also demonstrates a measurement that is acceptably immune to room effects

Fig 4 – Impulse response

Here the impulse response is shown. The rise time here includes the sound card latency, which is common to all the measurements. The impulse signal starts at just before 1 ms and the peak is reached at 1.08 ms. In this experiment we are concerned with the rise time, from the moment the signal starts at 1ms until the peak is reached. What happens after this point is beyond the scope of this article.

When mass is added

The next step was to add mass to the cone until the frequency response showed a significant effect on sensitivity. Neo magnets were used. Each disc is 10mm in diameter and 3mm in depth. These are attached to either side of the cone at various random places.

Fig 5 – Frequency response change with mass added (red). The response without mass loading is shown in black. Sensitivity is reduced by about 3 dB.

Mass loading has reduced sensitivity by around 3 dB.

The performance now looks quite poor, but is the impulse response rise time altered? Does the mass slow down the cone?

Fig 6 – mass loaded impulse response.

Fig 7 – overlaid impulse response – original (black) and mass loaded (red).

When overlaid, it becomes clear that the rise time is identical.

The impulse response is not entirely the same, but all the peaks and dips all occur at the same points on the time scale.

It has previously been argued by Dan Wiggins, audio engineer and founder of Adire Audio, that inductance and not mass, is a more useful indicator of transient response. To demonstrate this, an inductor was added. The inductor adds a first order rolloff except where affected by driver impedance.

Fig 8 – An inductor is added with a value of 2.5 mH. Roll off begins around 200 Hz.

Fig 9 – impulse response is significantly altered by the inductor.

A 2.5 mH inductor was added and it can be seen that there is an impact on frequency response as well as the impulse response. We can see there is a small delay in the rise time. The signal is delayed -  you can see that the impulse starts slightly later. The rate at which the peak rises is altered and the peak itself is also less transient. This is related to the filtering nature of the inductor.

Next the inductor is removed and DSP filtering is applied to match the frequency response.

Fig 10 – Black (initial test). Blue (inductor added). Green (DSP).

The DSP has achieved a close match in response. A first order low pass was applied and its corner frequency adjusted until a close match was achieved.

Fig 11 – Impulse response of the inductor vs DSP filtered response.

We can see the impulse response is so close that one thing becomes clear. The frequency response and impulse response are intimately tied together. It does not matter whether an inductor or DSP filter is used, both will have the same impact on the impulse response where their transfer functions are matched.

Now we apply a low pass filter so that the bandwidth is narrowed. Now it starts to resemble the response of a subwoofer, yet it should be noted that we are using a low mass driver.

Fig 12 – Raw response (black) vs DSP filtered response (grey).

The filter used here is a 2nd order Linkwitz Riley low pass filter at 80 Hz.

Fig 13 – Impulse response – raw (black) vs DSP filtered (grey)

Now we are starting to see a much more significant effect. The peak now occurs at 1.9 ms. As we move the filter down lower and use steeper filters, this effect becomes more dramatic. In a more extreme case, we apply an 8th order low pass at 40 Hz, to enable the subwoofer to simply extend the main speakers lower.

Fig 14 – DSP filtered (magenta) – Linkwitz Riley 4th order @ 40 Hz low pass.

Fig 15 – Impulse response

In order to see the impulse response with the very low bandwidth signal, the time domain scale had to be changed – it now spans 10 ms. The peak now occurs around 5.7 ms and this is as if the woofer were moved two metres further back. If using the kind of steep slopes that DSP allows, we can get a delay that is in the order of 10 metres!

What does all this mean?

By now it should be clear that mass is not something we should worry about. A transducer design engineer is very interested in the moving mass of the driver, but the concern is primarily related to matters of sensitivity and suitability for the job. Drivers intended for deep bass extension will tend to have a higher moving mass, often with lower sensitivity and a corresponding larger and heavier voice coil with a greater power handling. The mass alone does not tell us a great deal about the driver. In terms of the impulse response and more specifically, the rise time, mass is insignificant. Inductance is a factor, where woofers with a high inductance will tend to have a restricted bandwidth. However, what we can see in this experiment, is that the frequency response has a strong relationship with impulse response. A subwoofer has a very narrow bandwidth, although this is also strongly influenced by the low pass filter and how it is integrated. The result is that the time taken for it to reach its impulse response peak becomes extended. This is due to the inherent nature of the signal that is fed to the sub. It can be seen that there is no such thing as a fast sub in objective terms. Due to the limited bandwidth signal, a subwoofer is inherently slow. This has nothing to do with the moving mass of the driver.

What if a subwoofer actually does sound “slow?”

If a subwoofer sounds slow in the subjective sense, don’t blame it on the mass of the driver. There may be a problem with how it is filtered or integrated. The problem might reside in room modes. It’s also possible that the subwoofer itself is not up to the task. There are many possibilities, but its extremely unlikely that the moving mass of the driver could the cause of the problem.

StereoNET Discussion Thread.

About the Author

Paul Spencer is a StereoNET Technical Contributor. Paul is a long time StereoNET member, and owner of Red Spade Audio, specialising in Room Analysis and Custom Audio Design.
For more information visit http://www.redspade.com.au/audio/