Sound diffusion systems - Resonant frequency of a loudspeaker

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When an elastic system is subjected to an oscillating stimulus, it reacts differently depending on the frequency content of the stimulus. In particular, an elastic system will begin to oscillate when the frequency of the stimulus approximates the system's resonant frequency. Every elastic system in fact has its own resonance frequency which can be calculated by using mathematical formulae which describe the quantities involved in the system itself.

Let's now move on from theory to practice. Let's imagine that our elastic system is a loudspeaker (so, a system composed of different parts: membrane, coil etc.), which will have its own resonance frequency which in this case we'll consider to be 40 Hz.

By applying a sinusoidal electric signal to the loudspeaker and varying the signal's frequency, we will see that until the signal's frequency is distant from loudspeaker's resonance frequency, the loudspeaker's membrane will not be moved (or perhaps only a little). When we reach a frequency of about 40 Hz the membrane also begins to oscillate at this rate, and we will begin to hear a sound coming out of the loudspeaker which corresponds to the frequency of the applied electrical signal.

The following diagram shows the amplitude of the oscillation in question, stimulated by a signal with variable frequency:

Sound diffusion systems - Stimulation of an elastic system

Stimulation of an elastic system

We can see how the amplitude of the oscillations is at its highest in proximity to the resonance frequency, whereas elsewhere it is almost absent. The figure also shows the phase-diagram of this elastic system, which highlights how frequencies greater than the resonance frequency are subject to phase inversion (a phase displacement of 180 degrees implies a polarity inversion, in other words, a phase inversion). Naturally this situation is highly undesirable for a loudspeaker which should neither introduce variations to the input signal nor a phase inversion in the frequency band it has to reproduce. Indeed, the phase diagram of a loudspeaker would never have such a rate, which has been used as an example to highlight once again the issues, which are easily overlooked, concerning the phase's rate.


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