Resonance vs Time

MaVo

Member
2006-01-07 12:40 pm
Hi there, i have got a question about resonances. First, a bit of information, to establish a context.

1) From Wikipedia: "Acoustic resonance is the tendency of an acoustic system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency) than it does at other frequencies."

2) If you open the following link and scroll down a bit, you can see a picture of a waveform. This is a tone generated by a helmholtz resonator, excited with the hand. This picture shows that resonances not only affect the frequency domain, but also have a amplitude decay in the time domain.

http://www.phys.unsw.edu.au/jw/Helmholtz.html

3) In addition to that, Siegfried Linkwitz stated: "I did not consider alternate approaches to subwoofer design as acceptable for meeting my goal of accurate sub-bass reproduction. This includes vented, passive radiator and acoustic bandpass woofers. They all rely on resonant energy storage to increase efficiency and to reduce size."

Conclusion: Resonances seem to be a bad thing, not because they alter the frequency response, which simply has to be included in the design, but since they have a time decay characteristic. The energy put into the system radiates out of it over time. A tone which was in the original signal and lies in the resonant frequency band, will sound longer than in the original signal, which should be some kind of distortion.

Question: Could one conclude, that a closed box with a low q has the best time behaviour of all designs? How can one evaluate the effect of the resonances on the sound quality?
 
MaVo said:
Question: Could one conclude, that a closed box with a low q has the best time behaviour of all designs? How can one evaluate the effect of the resonances on the sound quality?

No.

Or... It depents on how you define "best". I would define it like that the best time behaviour (or any behaviour) is the one that gives the best perceptual reproduction of the sound.

One could of course define it as the shortest impulse response or the shortest decay time, but that is not the same thing. For example, a tweeter has a much shorter decay time than a full range loudspeaker. Still I prefer the fullrange when I listen to music, a single tweeter sounds a bit thin :D.

I think that people put too much attention to the impulse or step responses. It is very easy to do mappings to the perception of the sound that simply is not there.

Further, as soon as the Q is lower than 0.5, the system does not "ring" at all, so even if ringing per se would be bad, there is definitely a lower limit at Q=0.5.

Of course narrow resonances, with high Q values are never good. But there is an optimum, typically in the range 0.2-1.3 loosely speaking, for most designs.
 

ScottG

Member
2003-02-04 12:23 am
US
What SL (and many others) seem to have problems with are complimentary resonant systems. After all, the driver itself is a resonant system.

Anyway, that complimentary or secondary system will:

1. Increase linear decay problems at and near its resonance. (i.e. its poorly damped in this region.)

2. Increase overall time delay due to phase shifting. (..group delay just shows the sum of the woofer's delay with the secondary resonant system.)

As to issue #1:

Sure, its disadvantageous.. BUT its fairly narrow in bandwidth AND it can be (depending on the tunning freq.), below the range of most fundamentals. Moreover - see Advantages #1 below.

As to issue #2:

Time delay becomes increasingly less audible as freq.s lower, so again - IF the tunning freq. is low and the peak level of group delay isn't horrendous, then its likely to be effectively in-audible to most listeners.

(CAUTION: Note however that various bandpass systems violate to some degree most of the limiting conditions above.)

There are however several *Advantages* to a secondary resonant system:

1. The woofer's normal in-box resonance is now being damped by the secondary system. Normally such a system will have a resonance HIGHER in freq. (than one with a secondary resonant system) - and often in the range of fundamentals. Now however that woofer is being damped in that region, providing a greater measure of control with less distortion (linear and non-linear) than would otherwise occur at and near the driver's resonance in the enclosure. (..again though, a bandpass enclosure typically has a higher tunning freq. and as a result is often worse in this respect.)

2. Depending on the type of secondary resonant system, linear decay ABOVE the resonant tunning freq. can be better than the driver itself in this passband (..when normally operated in a sealed enclosure). (Here we are describing a GOOD vent design, as opposed to a passive radiator which has compliance problems of its own. Such a design requires an extended bandwidth and typically requires a low tunning freq..)

3. Finally, the additional "gain" in amplitude at lower freq.s provided by the secondary system allows for less overall driver excursion for a given input level (..though it may require a great deal more current output from the amplifier). This in turn results in less overall non-linear distortion at low freq.s versus a typical sealed system's radically increasing non-linear distortion levels.

IMO, the worst thing about a *good* design using a secondary resonant system is that below that system's tunning freq. the output level drops considerably in comparison to the average - AND effectively unloads the driver (..which can radically increase non-linear distortion if a near average fundamental appears at that extreme low frequency). (The former is always a problem, the latter *can* be a problem.)