Resonances

General Resonances are a cause of distortion, i.e. of deviations in sound generation compared to the input signal. They are energy storage effects that occur at certain frequencies in diaphragms and loudspeaker cabinets and create errors in music reproduction. Frequency filters and enclosures are therefore designed to minimize resonance. Every resonance also causes a temporal shift of the sounds to be transmitted. Resonances sound extremely aggressive and smear the sound image, transparency is lost. The same applies to intelligibility. As energy stores, resonances are temporally inert, they cannot spontaneously arise or disappear. Thus, they only become fully apparent in the steady state. During the transient of an impulse, on the other hand, the resonance is still charged with energy and only becomes noticeable with a delay. This removes energy from the signal. The resonance case of the oscillating system loudspeaker contains a time variable. Thus the high pass function is not constant. When measuring the impedance of a loudspeaker over time, it can be seen that the impedance curve is initially linear at the resonance frequency and the typical impedance rise only develops over time. When measuring with sinusoidal periods of different frequencies (dynamic measurement), it can be seen that the ratio of the first to the second half-wave is also not constant, but that the first half-wave shows a mainly radiation resistance-dependent curve, while the curve of the second half-wave is already determined by the influence of the resonance of the system. When the pulse decays, the energy of the resonance is discharged again, so that the decay is delayed and the signal is stretched in time. (An illustrative example of resonances as energy storage is also the microwave grill. Here, food is irradiated with the resonant frequency of water, which resonates with it, absorbs the energy and heats up. Since water is the largest component of any food, this heats the food as a whole)

Myro Elypticon'

Myro Wild Thing II

Membrane resonances The diaphragms are acoustic weak points of the cabinet: they are thin, permeable to sound, and resonate. Since diaphragms are not ideally stiff, outer diaphragm sub-surfaces resonate differently than inner ones, and do so vaguely chaotically. In addition, structure-borne sound vibrations propagate within each membrane material, which have a different sound velocity than the sound in the air. This leads to a complex interaction at certain locations of the membrane or even the edge suspension. Any material that is vibrated will resonate at its natural resonance(s), that is, it will respond to excitation by a spectrum of natural vibrations. This spectrum gives the loudspeaker diaphragms their inherent sound. The excitation can be caused by a mechanical force transmission or by acoustic energy from outside (sound waves). Resonances can already be excited by low energy. The resonance case, no matter what kind, must be avoided at all costs! The general requirements for a loudspeaker diaphragm are: it should essentially be light, stiff and have a high internal damping. Since these requirements contradict each other constructively, diaphragm materials are always subject to compromise. Every loudspeaker diaphragm generates diaphragm resonances. The number of resonances and their characteristics vary greatly between different types of drivers and diaphragm diameters. With hard diaphragms the resonances are in a higher frequency range than with softer diaphragms. They have a lower internal damping, but vibrate piston-like in the actual useful range, without resonance phenomena. Partial vibrations of hard diaphragms usually only occur above the main operating range. They can be very pronounced and very complex. In any case, it is helpful not to push these drivers to the limit and rather space the crossover frequencies one or more octaves apart. With an extremely stiff voice coil former (e.g. titanium), a favourable starting range at the diaphragm, an extremely stiff diaphragm (ceramic, diamond, beryllium) and a high magnetic field saturation in the air gap the direct coupling of the drive energy to the air is excellently possible with cone drivers. Soft membranes have a high internal damping, but tend to produce partial oscillations with their complex resonance phenomena in the actual useful range. Diaphragms with a high internal damping oscillate less strongly on their own resonances than drivers with low internal damping. However, the diaphragm resonances are usually in a lower frequency range, in the actual useful range of the chassis. When selecting drivers, attention should be paid to: 1. the oscillating system of mass, suspension and electromagnetic drive as well as 2. the deformation of the membrane (as well as the surround and spider) and 3. the diaphragm resonances.

Membrane resonances are a complex phenomenon. They essentially produce the inherent sound typical for a membrane material and can be time-variant or time-invariant. Only in the latter case can the Myro-typical frequency filters be used for correction.
If you want to eliminate the inherent membrane sound, more or less complex filters are necessary. Eliminating a disturbing diaphragm resonance always sounds better than not doing it. If a chassis had a completely damped natural resonance, then its transmission curve would correspond to the effective part of the radiation impedance. The filter circuits for this are not a problem, but critical loudspeaker drivers are. In some cases impedance minima below 4 Ohm can occur. However, these are usually narrow-banded and in frequency ranges where little power is demanded from the amplifier. The diaphragm resonances are not the same at all dispersion angles or have any effect at all. If they are corrected at a certain dispersion angle, i.e. in relation to a certain point, this correction may well turn into the opposite at other angles.
The result is a loudspeaker with practically no distorting inherent sound. (If the inherent sound of the diaphragms cannot be completely eliminated, types with the same (inherent) sound often blend together better. The partial ranges of the transmission spectrum then sound similarly coloured and this gives an impression of coherence, of harmony.) This is the prerequisite for there being no tonally disturbing colourations and the loudspeaker thus no longer being perceptible as an intrinsic sound source. If the sound sum is correct, together with the tweeter and eentually used bass, this applies to the entire loudspeaker, provided of course that no other inherent noises such as cabinet resonances (interior reflections and resonances / cabinet material resonances) or other buzzing and rattling noises become noticeable.

With diaphragm materials that are stable over a long period of time, the diaphragm resonances also remain quite stable in frequency and quality. Diaphragms, however, that are sensitive to temperature and especially humidity or that tend to corrode, the conditions are less stable. Such membranes often exhibit resonance behavior that is time-variant and thus difficult or impossible to correct. By time-variant is meant here that a diaphragm resonance first settles, then collapses due to counter-phase oscillations and then revives, whereby as a rule no stable resonance frequency is established in this process. All this happens within a few milliseconds. Such a process cannot be corrected by a filter.
Broad-range drivers are a special case among drivers and contain exclusively resonances over a wide range in the high frequency range as part of the concept, where they provide a level but no musical information.

Mundorf AMT26-Myro-V2

Hard membranes

The use of hard diaphragms provides better power transfer to the air and thus improves impulse response. However, if one uses the usual standard filters in the crossover, such as non-matching 1st order filters (6 dB/oct) or even 2nd (12 dB/oct) or 3rd order impulse destroyers (18 dB/oct), then the advantage of hard diaphragms is nullified. The result is harshness of a special kind. The impulse distortion of these filters and delay errors within the construction, as well as the combination of drivers that do not match each other, produce distortions that sound hard. But these can also be produced with softer diaphragms.
Hard diaphragms shift the resonances to the upper end of their transmission range or beyond, but there they are more pronounced with extremely high Q and require appropriate correction filters. The frequency response usually drops off before this point, thus almost corresponding to the ideal typical transfer function of a driver of this size. A closer look at the result, however, shows that even with higher order filters, the diaphragm resonances will cut through and produce the typical long after resonance. These are also harshness, a sharp buzz that is added to the sound with each excitation. Hardening is therefore usually a result of errors! If, on the other hand, the advantages of stiff diaphragms are used and their resonances are damped, the speakers sound neutral. Simplified: the harder the material, the higher the diaphragm resonances. It is rare to find a clear relationship between the fundamental wave and harmonics and subharmonics. In the case of diamond, beryllium and ceramic diaphragms, however, these relationships are recognizable. The partial oscillations of a membrane, i.e. the natural oscillations of partial surfaces of the membrane, are time-variant and cannot be described with simple models.
In the case of stiff materials, the resonances oscillate evenly over time. In the waterfall diagram, a uniform, frequency-stable "mountain range" can be seen. The step response accordingly shows a uniform ripple of the graph. A notch filter eliminates this ripple completely, whereby it is to be noted that the excitation takes place by an extremely broadband signal, in which all frequencies of the transmission bandwidth of the chassis are contained. In addition, attention must be paid to series scattering.

Soft diaphragms

Soft diaphragms with high internal damping also exhibit a variety of natural resonances. They are however also more strongly damped, therefore with smaller quality and usually also in lower frequency ranges to find than with hard diaphragms. They are therefore in the transmission range and sometimes even give the impression that the usable transmission range is more extended towards high frequencies. Soft diaphragms also react more critically to bead resonance (resonance of the edge suspension) than hard diaphragms.
The partial oscillations are extremely complex and, due to their time variance, cannot be clearly reproduced and reduced by filters on the input side. In addition, there are partial oscillations that occur together with the diaphragm resonances. This results in a time-variant mix with an upward and downward swelling over time. Partial oscillations occur with a minimal delay and do not directly affect the transient response. In their generation process, the tension of the "springs" of the individual membrane segments takes energy from the forward motion. This is mainly a problem of soft and not very stiff diaphragms in general. The voice coil dips into and deforms the diaphragm in compliant diaphragms, especially in fast, impulsive processes. As a result, energy is lost, the impulses are delayed and the energy introduced is converted into heat or subsequent residual sound waves that interfere with the direct sound.
A common phenomenon with soft membranes is the so-called midrange (edge) resonance.

The plush diaphragm
... does not exist for good reasons, but it would have an advantage. After all, coaxial speakers are popularly used as an approximation of the point source and have undeniable advantages in that regard. But they also contain the dilemma between the advantages and disadvantages of hard and soft diaphragms, because they always have one problem: the tweeter gives impulses and frequencies to the midrange / bass diaphragm in the centre at full level, so that the diaphragm is struck like a sound bowl. It excites the diaphragm resonances of the midrange / bass diaphragm and these movements build up to resonances. This causes the diaphragm, as the sound source, to radiate sound waves that add or subtract, depending on the time correlation to the high frequency sound. We can see this in the diagrams.

The harder the material, the more pronounced the effect. And unfortunately these diaphragm resonances of the mid-woofer diaphragms lie exactly in the transmission range of the tweeter. So coaxial designs require more or less soft diaphragms to limit the effect. But since hard diaphragms are actually acoustically advantageous, this conflict of objectives cannot be resolved. A plush diaphragm would therefore be advantageous, considered from this aspect alone.
The excitations by the tweeter sound pressure can be compared on the frequency scale with those shown by the cone when excited via its own voice coil. This is because when the tweeter is measured on its own, it excites the diaphragm resonances of the mid-woofer cone. This causes the diaphragm to move and these movements build up to resonances. As a result, the diaphragm, as the sound source, emits sound waves that add or subtract, depending on their temporal correlation to the high-frequency sound. This effect can be demonstrated by measurement.
The problem will always be noticeable when drivers are placed close together, at least one of which operates in the resonance ranges of the other. However, the sound pressure of the excitation is many decibels lower than with a coaxial chassis.

Magnesium membrane

Aluminium diaphragm

Reed-Paper-Membran

The pictures on the left show measurements of Seas coaxial drivers as used in various models, e.g. the Myro Coax Monitor. Here you can clearly see the correlation of the midrange diaphragm resonances with the non-linearities of the high frequency response. Wherever the midrange diaphragm forms a resonance, there is an interaction with the sound radiated by the tweeter. The resonance points each have a specific amplitude phase response and are related to the amplitude phase response of the tweeter. The effects are very complex. Example: Where there is a peak (resonance) of the midrange diaphragm (black) in the reed-paper diaphragm, there is an interaction with the tweeter sound and in the frequency response of the tweeter we see exactly (almost mirror image) in the ripples of the midrange diaphragm corresponding ripples in the tweeter frequency response. These are the interactions of the resonating midrange diaphragm with the tweeter sound.

Source: Seas Company, www.seas.no

Manger transducer'
A special type of soft diaphragm is the Manger transducer. Here, the deforming diaphragm is part of the concept by forming bending waves. Thereby a part of the kinetic energy is stored in the membrane or converted into heat there. Of course, the diaphragm of a Manger transducer also has resonances, just as the entire vibrating system has one or more self-resonances. There are some phenomena between the inner membrane part (inside the big voice coil) and the area outside. And it is on these resonances that the system oscillates after excitation - and that is exactly how it sounds. There are also restoring forces there, and the diaphragm eventually returns to its original shape.

Summary

Well developed hard diaphragm drivers are usually superior to soft diaphragm drivers in all points in their range of application and have only one disadvantage: the weakly damped diaphragm resonances at the upper end of the transmission range. If these are left undamped, these drivers sound like many know them: hard, harsh and ringing and rattling like a bicycle bell. This is the breeding ground for many prejudices. If a tweeter is placed in the centre (coaxial), this resonance is extremely strongly stimulated by the tweeter, from the outside, and is even extremely reflected in the frequency response of the tweeter.
To damp undamped diaphragm resonances is possible mechanically (applying damping mass = heavy diaphragm) or electrically by equivalent filters, but very complex and to be measured in the production series (series dispersion of the chassis). The increase of the diaphragm weight is equivalent to an electrical low pass, thus it acts like components in the signal path. The partial oscillations of a diaphragm are shifted towards lower frequencies by the application of a damping mass and their effect is weakened. The transmission path of the chassis looks accordingly. The drop to higher frequencies becomes stronger and the phase more lagging. The linearity increases if it is done correctly overall.
One should be careful, however, that the diaphragm suspension and the overall design of the drive can tolerate a higher moving mass, because originally they were designed for a lower moving mass. On the other hand, an increase in distortion would also be expected, especially if the diaphragm mass dips into the nonlinear regions of the rim suspension and spider at larger strokes.

Can sensor control help?

Some powered speakers use sensor control to reduce driver nonlinearities. Sensory controls can be added to correct some phenomena. They should only act in "real time" if possible. However, sensors only detect certain characteristics at the location of the sensor. What happens at a distance of several meters as an interaction of all systems, e.g. delay differences at the listening position, cannot be captured by this. Even if every single membrane would behave completely correct, equal to the input signal, this would not be an indication for the correct sound sum of the systems.
The same applies to the effects (sum / difference over time) of partial vibrations of the membranes at listening distance, the radiation impedance of the drivers in the cabinet, the secondary sound waves due to sound diffraction etc.. In principle, they cannot be corrected. A sensor control can only control what it senses at the point of control. If the sensor is a microphone at the diaphragm, it can only record the sound pressure curve at this point and feed it as information into the control. However, since diaphragms are not ideally stiff, outer diaphragm parts vibrate differently than inner diaphragm parts. In addition, structure-borne sound vibrations propagate within each diaphragm material, which have a different sound velocity than the sound in the air. This leads to a complex interaction at certain locations of the membrane or even the edge suspension. The sensor does not notice much of this. The sensor also does not notice sound components that become secondary sound waves due to diffraction at the chassis or cabinet edges. Therefore, a control is ineffective here.
Furthermore, dynamic time errors caused by the frequency filters should be avoided. Otherwise the whole control is useless.

Myro Concert Monitor

Cabinet resonances Unlike diaphragms, cabinet resonances are usually, but not always, undesirable. The lower cut-off frequency can be achieved in an open, closed or in an enclosure with a resonance principle (bass reflex / transmission line etc.). The often used bass reflex principle specifically excites a resonance frequency in order to amplify the sound pressure in the low frequency range. The way the bass reflex principle works shows that such a resonance system needs a certain amount of time to settle in. During impulse reproduction, the sound energy of the resonance system is not yet available! Transmissionline and Backloaded Horn also use resonances for sound amplification. However, the following applies to all resonances: They generate unmodulated sound. They generate sound pressure, but do not contain any musical information, because the sound is generated uncontrolled and does not follow the music signal. Resonances therefore do not extend the transmission range for music. This can only be achieved with a larger diaphragm area. In addition, other aspects determine The design of the cabinet, among other things to avoid unwanted resonances in the cabinet. Aural resonances Resonances characterize all listening experiences, including natural sound events, because they are not only part of technical reproduction systems, but also of the human auditory system. They are thus a component of every natural auditory impression. Resonances form due to the length of the outer auditory canal and lead to increased sensitivity in certain frequency ranges. In the range of the human auditory spectrum, there are three resonance points that shape the auditory sensation. They lead to the fact that the sensitivity of the auditory system, which decreases due to mechanical inertia, is compensated for at high frequencies and even increases at 4 kHz. The technical literature offers further descriptions of this, on which the construction of loudspeakers has no influence. Room resonances Resonances are part of almost every room due to parallel walls, floor and ceiling. They also make time-correct hearing in the room difficult and change the information contained in the sound like any other resonance.

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