Sound Reflections in Indian Stepwells: Modelling Acoustically Retroreflective Architecture

Round 1

Reviewer 1 Report

This paper reports the study of the retroreflective behavior of a particular type of Indian building, called Stepwells. These buildings are an important architectural heritage of India and the world and any study that analyzes their architectural, structural and usage characteristics, information that has often been lost over the centuries, is important and contributes to the conservation of these monuments. On the other hand, these buildings can also be a source of inspiration for modern designers. From the point of view of acoustics, some ancient buildings have special features and there must be more to discover.

The paper is well written, easy and pleasant to read despite its length. The authors reports the work done in great detail. Important characteristics of the Stepwells and the numerical method used for the analysis were discussed. The results are abundant and show that the reflected acoustic energy is concentrated in some points of interest. However, the phenomenon occurs at a relatively high frequency (2 - 4 kHz), which is a high frequency from the point of view of human speech. The results were obtained by an approximate numerical method, based on finite differences, reported by the same research team in a previous article. It was clarified that the method requires many approximations, as expected due to the complexity of the problem. Therefore, the numerical results can only be validated with experimental measurements. The authors mentioned that the COIVD-19 pandemic prevented the fieldwork from being carried out.

In my opinion, there is enough evidence of a special acoustic behavior in the analyzed Indian Stepwells and the article deserves to be published. The experimental results may be presented in a second article.

The authors say that “Stepweels are designed for water access, not acoustics”. The resulting acoustic characteristics are incidental. The use of these buildings as meeting places, similar to theaters, seems to be possible. Therefore, if they were designed for this purpose as well, it is very likely that the original Indian designers were concerned with acoustics, as they were in other buildings. If the Stepwells were designed only for water storage, does it make sense that they all have such similar architecture?

Please, revise the following issues:

• Line 106: probably the word “acoustics” is redundant.

• Lines 228-229: the dependence on size and distance of the diffraction loss cannot be directly established by equation 1.

• In figure 9, blue and green lines are mentioned but they are not visible.

Author Response

REVIEWER point 1: This paper reports the study of the retroreflective behavior of a particular type of Indian building, called Stepwells. These buildings are an important architectural heritage of India and the world and any study that analyzes their architectural, structural and usage characteristics, information that has often been lost over the centuries, is important and contributes to the conservation of these monuments. On the other hand, these buildings can also be a source of inspiration for modern designers. From the point of view of acoustics, some ancient buildings have special features and there must be more to discover.

The paper is well written, easy and pleasant to read despite its length. The authors reports the work done in great detail. Important characteristics of the Stepwells and the numerical method used for the analysis were discussed. The results are abundant and show that the reflected acoustic energy is concentrated in some points of interest. However, the phenomenon occurs at a relatively high frequency (2 - 4 kHz), which is a high frequency from the point of view of human speech. The results were obtained by an approximate numerical method, based on finite differences, reported by the same research team in a previous article. It was clarified that the method requires many approximations, as expected due to the complexity of the problem. Therefore, the numerical results can only be validated with experimental measurements. The authors mentioned that the COIVD-19 pandemic prevented the fieldwork from being carried out.

RESPONSE point 1: The reviewer's summary/overview demonstrates a strong understanding of the manuscript's content and purpose.

REVIEWER point 2: In my opinion, there is enough evidence of a special acoustic behavior in the analyzed Indian Stepwells and the article deserves to be published. The experimental results may be presented in a second article.

RESPONSE point 2: We recognise that the lack of fieldwork results limits this manuscript, but we have tried our best with what was possible. We are pleased that the reviewer takes a balanced view on this issue.

REVIEWER point 3: The authors say that “Stepweels are designed for water access, not acoustics”. The resultingacoustic characteristics are incidental. The use of these buildings as meeting places, similar to theaters, seems to be possible. Therefore, if they were designed for this purpose as well, it is very likely that the original Indian designers were concerned with acoustics, as they were in other buildings. If the Stepwells were designed only for water storage, does it make sense that they all have such similar architecture?

RESPONSE point 3: These are really interesting questions, but difficult to deal with without resorting to speculation. Clearly stepwell design is motivated by architectural spectacle - so there's definitely a visual design element (it's not just water storage!). The concept of them being similar to theatres/meeting places is interesting, but it does not seem to be a theme in the social documentation of them in the main literature. Some are/were used for religious purposes, which may come close to the reviewer's thinking. With regard to the acoustics, there are some anecdotal reports of interesting acoustics. Some people report that they have the auditory impression of being followed (which is explained by reflections) in some stepwells but these reports are in tourist articles, not scientific studies. Livingstone briefly describes Chand Baori's acoustics for monastic chanting - but it is unclear whether her writing is based on observation or speculation. Unfortunately no prior study has been done on stepwell acoustics so it does not appear to be possible to develop these ideas currently. It seems likely that there is more to study in the future!

REVIEWER point 4: Please, revise the following issues:

• Line 106: probably the word “acoustics” is redundant.

RESPONSE point 4: thanks - the redundant word 'acoustically' has been deleted.

"In this way, stepped ponds provide potentially rich cases for retroreflective room acoustics,..."

REVIEWER point 5:

• Lines 228-229: the dependence on size and distance of the diffraction loss cannot be directly established by equation 1.

RESPONSE point 5: we have clarified that it is indicated indirectly.

"(as indicated indirectly by Equation 1)"

REVIEWER point 6:

• In figure 9, blue and green lines are mentioned but they are not visible.

RESPONSE point 6: Unfortunately the PDF failed to render MATLAB chart elements that had alpha<1, so some charts were not displayed correctly in the review PDF. However, the original EPS files submitted do display all the chart elements correctly. We have re-inserted all EPS images in the document, using a different method. However, we recommend using the EPS files provided for the publication figures.

Thank you for spending time with this manuscript.

Reviewer 2 Report

The manuscript presents a simulated study of various step-wells situated in India. These wells/ponds have a historical significance and thus their acoustic analysis seems interesting to readers.

I will suggest if the authors could perform an experimental study of at least one such well.

> In the modeling and simulation section, the term 'dx' needs a proper explanation. 

> cite a reference for equation 2.

> Most of the models suggest a significant response in higher frequencies. 

Authors should provide the reason behind it. 

Author Response

REVIEWER point 1: The manuscript presents a simulated study of various step-wells situated in India. These wells/ponds have a historical significance and thus their acoustic analysis seems interesting to readers.

RESPONSE point 1: The study includes both theory and simulation (not just simulation). Thank you - yes we also think that the article should interest readers.

REVIEWER point 2: I will suggest if the authors could perform an experimental study of at least one such well.

RESPONSE point 2: We note that all reviewers appear see the benefit of field work. Reviewer 1, however, believes that the manuscript is publishable without - leaving fieldwork for a subsequent study. Reviewer 3 does not directly express an opinion (but comments that validation is not in the manuscript). We, of course, agree with the reviewers that experimental fieldwork is the next step in our study of stepped pond acoustics, and hope that the reviewers and editor sees the value of the detailed work that we have done. In our opinion, Reviewer 1 has given a careful and balanced analysis of the manuscript, and appears to have weighed the issues up most convincingly. We also point out that the issue of no fieldwork was discussed with the Guest Editor prior to preparing this study. Fieldwork is not possible in the 10 day review response period.

REVIEWER point 3: > In the modeling and simulation section, the term 'dx' needs a proper explanation. 

RESPONSE point3: We have rephrased this sentence, explaining that it is the cubic voxel width.

"It was voxelized with a cubic voxel width (dx) of 9 mm,..."

REVIEWER point 4: > cite a reference for equation 2.

RESPONSE point 4: We have rephrased the sentence after Equation 2 to reiterate that the the source of the equation is reference 8.

"This is a simplification of the theory in [8], neglecting the absorption coefficient of the surface and atmospheric loss, to match the FDTD simulation."

REVIEWER point 5: > Most of the models suggest a significant response in higher frequencies. 

Authors should provide the reason behind it. 

RESPONSE point 5: We are puzzled by this comment because the manuscript provides the reason for the high-frequency bias in retroreflection at the outset (first paragraph of Section 1.1 'Introduction to Acoustic Retroreflection in Architecture'). The reason, of course, is diffraction loss, which is explained as having a 6 dB/octave slope below fR/2, according to both theoretical expectations and measurements (see, for example, Rindel's article, ref 14). This point is developed further in the manuscript, both by detailed calculation of diffraction coefficients (using Kirchhoff-Fresnel integral method) and through the simple indicative approach of calculating fR/2, based on Equation 1. Furthermore, this finding is highly consistent with similar studies of acoustically retroreflective building facades, which are cited.

We have carefully considered whether more repetition of this is needed, but decided against it. The paper definitely includes the explanation, and provides further references for a curious reader.

Thank you for spending time with this manuscript.

Reviewer 3 Report

A specific research work.

Some trivial phenomena explanations must be omit.

There is no experimental validation of the numerical results.

In Fig. 9 there are not blue or green lines.

It is better if the applicable part of this research is clarified.

Author Response

REVIEWER point 1: A specific research work.

RESPONSE point 1: yes we agree.

REVIEWER point 2: Some trivial phenomena explanations must be omit.

RESPONSE point 2: Unfortunately this comment is enigmatic and vague, so we are really unsure of the reviewer's meaning. Thinking about the words 'trivial' and 'phenomena', it seems most likely that the reviewer thinking about the analysis of angle error and temperature gradient (because they are null hypothesis tests of phenomena - which might be regarded as trivial). However, we believe it is important to include these especially because of the lack of field validation - we need to know that the effect is robust, even if the phenomena seem trivial.

REVIEWER point 3: There is no experimental validation of the numerical results.

RESPONSE point 3: Yes that is correct, but there is comparison with analytic theory. This issue was raised prior to the preparation of the manuscript with the editor of the special issue, who agreed that this paper would be potentially suitable without fieldwork (which has been impossible due to COVID-19 restrictions, as stated in the manuscript). We think that we have done the best we can under this limitation, and have included analysis of the effect of geometric error and temperature gradient to provide some idea of how imperfect conditions may affect the sound propagation. Furthermore, the reviewer is referred to other comparable studies of acoustic retroreflection in architecture:

• Cabrera, D, et al. "An unusual instance of acoustic retroreflection in architecture–Ports 1961 Shanghai flagship store façade." Applied Acoustics 138 (2018): 133-146.
• Cabrera, D, et al. "Incidental acoustic retroreflection from building façades: Three instances in Berkeley, Sydney and Hong Kong." Building and Environment 172 (2020): 106733.
• Cabrera, D, et al. "Voice support from acoustically retroreflective surfaces." Euronoise 2021.

The above studies include both physical measurements and the same type of wave-based acoustic simulation - showing physical evidence of acoustic retroreflection with comparable architectural forms. Details of these studies show that FDTD simulation is highly effective as a simulation tool for this propagation phenomenon, with results compatible with measurements. To an extent, these studies validate the simulation method for this type of architectural acoustics situation, even if they are not specific to the stepwell cases.

We also refer the reviewer to Reviewer 1's more considered response to the manuscript, which weighs this limitation against other issues - including the bulk of evidence presented in the manuscript. We will do physical measurements when it is possible, as stated in the manuscript - and Reviewer 1 recognises that this would be appropriate as a subsequent paper.

REVIEWER point 4: In Fig. 9 there are not blue or green lines.

RESPONSE point 4: Thanks for pointing this out. The PDF image-rendering of MATLAB figures omitted any elements that had alpha<1, so unfortunately some figures were incompletely rendered in the review PDF. However, all figures were originally also submitted to the Journal as EPS or JPG, and these files do not have the image rendering error.

We have replaced all the EPS figure inserts in the document using a different method. However, we recommend that the Journal use the EPS files submitted.

REVIEWER point 5: It is better if the applicable part of this research is clarified.

RESPONSE point 5: Thank you, but this paper is not about applications - instead it is aiming to document an unusual acoustic phenomenon in highly distinctive historic/monumental architecture. We have provided a succinct overview of some application areas in Section 1.1 - including possibilities in multi-talker environments and auditoria. However the purpose of the paper is not applications of retroreflectivity.

We are preparing other manuscripts in the area of acoustic retroreflectivity that are focused on design and applications, rather than on describing historic architectural forms.

Thank you for spending time with this manuscript.

Round 2

Reviewer 2 Report

The revised version has incorporated all the suggestions .

It can be considered for next stage processings.

Reviewer 3 Report

I accept changes, now the paper sound is more scientific.