There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

Origins of Newton's laws of motion

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

Friday, June 7, 2013

3.16 Circuit analysis of the acoustical circuit in Fig. 35

 All postings by author previous: 3.15 Resonant scattering of waves - 1D up: Contents next: 3.16a Modeling the acoustic circuit with an electrical equivalent

3.16 Circuit analysis of the acoustical circuit in Fig. 35.

Keywords: circuit analysis, scattering, resonant, circulator

The string and acoustical circuits shown in the last two postings (Figs. 26, 35 and 36) can be analyzed conveniently with circuit analysis methods used in electrical engineering. In a string of postings starting with this one, we describe this analysis and graph the results. This analysis is done in a variety of ways to show the possibilities and also to cross check the results. In the posting 3.16a through 3.16g (also 3.18) we address the acoustical circuit in Fig. 35: we draw the equivalent circuit, analyze its response analytically, and then show the SPICE simulation of the circuit.

 Fig. 40. A snap shot of the animation, Fig. 35, of the previous posting.

The image above is a snapshot of Fig. 35 of the last posting. Incident waves are launched from the left, travel down the waveguide, through the circulator to the coupling hole of the resonator. There, the waves are reflected, travel back to the circulator, into the right waveguide, and finally to the absorber.

Analysis of this circuit is applicable to the many cases of one dimensional resonant wave scattering technology where the negative-going waves are easily separable from the incident waves. As pointed out in the last posting, it also applies to two and three dimensional cases where the angular distribution of the reflected waves is the same as the angular distribution of the waves radiated from the resonator mixing the two inseparably. This is the usual case in radar waves scattering off a large (compared with a wavelength) structure coated with a resonant layer or with LIDAR where extremely short wavelength light waves typically scatter off objects coated with molecules that act as resonant scatterers.