The Body: Compact and Flexible.

As a wearable device, it was necessary for the material to be flexible. Our initial idea was to make a silicon box by 3D printing. Upon further research, we realised that current technology does not 3D print silicon objects and those are made in moulds. The moulds would have to be specially designed for our box and echo chamber, which would be too costly for a project of this scale to produce only one copy of each item. Hence we decided on TPU as our flexible material. Although it is less flexible, it is much less costly and easier to produce.

The Echo Chamber: Initial Testing

The special component in our project is the Echo Chamber that is meant to amplify the sounds to be recorded by the microphone. The basic anatomy of the Echo Chamber includes a circular base where the diaphragm, a membrane that vibrates to pick up sounds from the chest cavity, is located, TPU walls, and a narrow neck at the top where our microphone is fitted. Unlike the standard 4.5 cm in diameter seen in commercially available adult stethoscope diaphragms, we aim for a 3.5 cm diameter for children which is found to be sufficient for effective auscultation. However, due to difficulties in 3D printing of small models, we started out testing for sound quality with scaled-up Echo Chamber models of 4.5 cm base diameter.

Our first testing phase included 5 different shapes of the Echo Chamber, most of them with the same height. Below are specifications of the shapes and out initial rationales for including them.

1. Deep cone (as in bell shape of normal stethoscope) – Control
2. Shallow cone – Reduced internal volume to amplify sound
3. Straight cylinder (concave wall with respect to the internal volume) – Sound concentration by surface curved in one direction
4. Dome shape (concave wall) – Enhance sound concentration by surface curved in two directions
5. Horn shape (convex wall) – Sound diffusion to even out reverberations and reduce interference

Results and the goings-on of our shape testing are elaborated in this subpage: Testing the Echo Chamber Shapes.

The Echo Chamber: Sound Energy Focusing in the Reverse Horn.

The reverse horn has been gaining attention as a sound absorption system for low-frequency broadband owing to an energy focusing phenomenon (Zhang et al., 2016, Liang et al., 2019). Sound energy focusing at the wedge-shaped tip of a solid beam has previously been demonstrated (Krylov and Parker, 1989). The gradually decreasing area, moving from the mouth to the tip of the reverse horn, resembles this non-linear structure. Sound waves travelling in the decreasing volume are bent and slowed down. Under ideal conditions, with the addition of suitable damping materials at the tip sound energy can be effectively dissipated (Kralovic and Krylov, 2007). This is now termed the Acoustic Black Hole (ABH) structure. Liang et al., 2019 theorised similar ABH properties in the reverse horn by drawing an analogy to the bottleneck effect on the flow of air particles. They posited that nearer to the tip of the horn, air particles are forced together, increasing the contact and friction between them. At some critical tip area, this contact is large enough to dissipate sound energy as heat energy. This bottleneck effect lays the foundation for sound absorption using the reverse horn.

How is this sound absorption mechanism relevant to our echo chamber? The answer lies in the sound energy focusing at the tip of the reverse horn. Zhang et al., 2016 suggested that only sound waves of lower frequencies, and thus longer wavelengths relative to the length of the reverse horn, can be focused at the horn tip. Higher frequency waves, on the other hand, are reflected by the walls of the horn. Liang et al.’s qualitative analysis demonstrated this by showing that at a tip-to mouth diameter ratio of 0.175, waves of frequencies 600Hz and below were effectively focused at the reverse horn tip, while 4000Hz waves were reflected back into the volume of the horn. Heart and lung sounds to be picked up by our stethoscope fall in the frequency range between 10Hz and 2500Hz, which puts their wavelengths (between 0.0136m and 3.4m) safely in the range that will not be reflected within the small echo chamber (20.5mm). In addition, their qualitative analysis suggested that sound absorption is more effective at smaller tip-to-mouth diameter ratios by comparing absorption at 2 distinct ratios 0.121 and 0.79. Our echo chamber design dictates a fixed diameter ratio of 0.234 between the tip and mouth of the reverse horn, so the prospect of sound focusing without dissipation at the horn tip where our microphone is positioned likely contributed to the capture of relatively stable sound amplitudes as seen in our test.

Beyond these theoretical analysis, however, the bottleneck effect and ABH properties show limited application to the performance of our echo chamber, due both to limited literature beyond these 2 studies, and to the lack of more accurate modelling of the relationship between horn length, wavelength, and tip-to-mouth diameter ratio. Experiments in these 2 studies were carried out using much larger reverse horns of lengths 200mm and above, as compared to our short echo chamber, while the frequency range is comparable to ours. This discrepancy prevents us from justifiably attributing this theory to the performance of our reverse horn echo chamber without further testing.

References:

Krylov, V. V, & Parker, D. F. (1992). Harmonic generation and parametric mixing in wedge acoustic waves. Wave Motion, 15(2), 185–200. https://doi.org/https://doi.org/10.1016/0165-2125(92)90018-W

Liang, X., Wu, J. H., Zhou, Z., & Chen, Z. (2019). Quantitative analysis of low frequency acoustic characteristics for reverse horn by bottleneck effect analogy method. Modern Physics Letters B, 33(16), 1–14. https://doi.org/10.1142/S021798491950177X

Zhang, Y. Y., Wu, J. H., Cao, S. H., Cao, P., & Zhao, Z. T. (2016). New acoustical technology of sound absorption based on reverse horn. Modern Physics Letters B, 30(34), 1650403. https://doi.org/10.1142/s0217984916504030