Topological Acoustic Sensing Using Nonseparable Superpositions of Acoustic Waves

Round 1

Reviewer 1 Report

The paper shows a method to sense a mass defect by measuring changes in geometric phase. They show that the shift in geometric phase due to the mass defect is sensitive to the loading condition. The theoretical model is accompanied by supporting experiments. The idea is novel and the concept, method, and results are well presented. I support publication after the following minor points are addressed:

1. page 5: the basis for a 9-dimensional Hilbert space is presented. However, the space of allowable waves is 3-dimensional and not 9-D. An explanation is required for why a 9D space is used/presented. It seems one cannot have  waves like e2.exp(i k_1 x) 

2. Page 6: Figure 3 caption appears twice. 

3. The authors assume 1+R=T. Will this condition hold always? For instance, if there is a local resonance at the defect and the incident wave has the resonant wave frequency? A brief explanation may be useful. 

4. The authors refer to Fig. 5b and 5c, but I do not see fig. 5c. 

5. Section 4: Why is the variation of the driving parameter r equivalent to that of a ribbon (that has no boundary? What is the similarity between r=0 and r=2? It seems the domain of r = [0,2] has boundaries: {0,2}. Some explanation will be helpful. 

6. The authors claim: "in the limit of infinitesimally small masses..... delta peak". This is very interesting but not obvious. It will be good to show this numerically: by considering a series of alpha values and showing the behavior as the defect mass decreases. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper developed a topological acoustic sensing method to sense mass defects in arrays of coupled acoustic waveguides. The authors provided both theoretical models and experimental results to validate this method. I have the following comments and questions for the authors:

1. The authors mentioned "We have verified experimentally that epoxy provides the dissipation needed to achieve complex resonant amplitudes", please provide supplemental data that support this statement.

2. The setup and conditions in the experiment should be defined and interpreted in more details, in related to the theoretical models. For example, please explain how "nonseparable coherent superpositions of acoustic waves" contribute to the sensing of mass defect in the experiments.

3. The authors mentioned "There is no theoretical limit to the magnitude of the mass of defects that can be detected". Did the authors test different mass in the experiments? What will be the impact of mass on the amplitude and spectrum?

Author Response

Please see attachment.

Author Response File: Author Response.pdf