Review Reports - On the Reflection of a Spherical Sound Wave from a Finite Size Surface

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study addresses the limitations of the long-used plane wave reflection assumption in geometric acoustics simulations, proposing an innovative spherical wave reflection approximation model. The authors successfully extended the classical mirror source method to handle surfaces of finite size and established the theoretical framework through clear physical explanations (such as combining the Babinet principle and radiation impedance). The paper clearly points out the importance of the spherical wave effect in hard surfaces, grazing incidence, and short-distance propagation, and applies the model to the classic problem of sound attenuation above the audience area, demonstrating good application value. The work logic is rigorous and makes a substantive contribution to improving the accuracy of room acoustic simulation.
1. Abstract Enhancement: It is suggested that the abstract should more clearly indicate that this study expands upon the core innovation points of Thomasson et al.'s work, namely, the first time that the spherical wave reflection model was combined with the complex radiation impedance of a finite-sized surface, rather than merely replicating Ingard's infinite plane solution. This can more accurately summarize the incremental contributions of the research.
2. Introduction Deepening: The introduction part mentions many pioneering works, but the commentary is somewhat brief. It is recommended to strengthen the comparison and discussion of the methods in Thomasson (1976) and Mechel's works, clearly indicating the differences and connections between the methods of this study and theirs, thereby more clearly positioning this work in the academic context.
3. Experimental Comparison and Discussion Expansion: In the comparison with the measurements by Meyer et al. in Section 5, the analysis can be more in-depth. In addition to the three assumptions listed, it is recommended to specifically discuss how these simplifications (such as simplifying the audience area to a box, using real impedance) may systematically lead to differences in calculations and measurements in specific frequency bands (such as high frequencies within a distance of 3-5 meters), and to explore their physical meanings.
4. Terminology and Expression Refinement: The term Q is referred to as "image strength" in the text (e.g., Section 5.2), but according to its definition (Equations 5 and 6), Q is essentially the spherical wave reflection coefficient. It is recommended to uniformly use more precise terms such as "spherical wave reflection factor" or similar terms throughout the text to avoid confusion with the concept of "source strength".

Author Response

Reviewer 1

1. Abstract Enhancement: It is suggested that the abstract should more clearly indicate that this study expands upon the core innovation points of Thomasson et al.'s work, namely, the first time that the spherical wave reflection model was combined with the complex radiation impedance of a finite-sized surface, rather than merely replicating Ingard's infinite plane solution. This can more accurately summarize the incremental contributions of the research.

Reply: The abstract in changed as suggested.

2. Introduction Deepening: The introduction part mentions many pioneering works, but the commentary is somewhat brief. It is recommended to strengthen the comparison and discussion of the methods in Thomasson (1976) and Mechel's works, clearly indicating the differences and connections between the methods of this study and theirs, thereby more clearly positioning this work in the academic context.

Reply: The introduction has been extended as suggested.

3. Experimental Comparison and Discussion Expansion: In the comparison with the measurements by Meyer et al. in Section 5, the analysis can be more in-depth. In addition to the three assumptions listed, it is recommended to specifically discuss how these simplifications (such as simplifying the audience area to a box, using real impedance) may systematically lead to differences in calculations and measurements in specific frequency bands (such as high frequencies within a distance of 3-5 meters), and to explore their physical meanings.

Reply: Further discussion and explanation of the results are added in Section 5.

4. Terminology and Expression Refinement: The term Q is referred to as "image strength" in the text (e.g., Section 5.2), but according to its definition (Equations 5 and 6), Q is essentially the spherical wave reflection coefficient. It is recommended to uniformly use more precise terms such as "spherical wave reflection factor" or similar terms throughout the text to avoid confusion with the concept of "source strength".

Reply: The concept of image strength was used by Ingard. But it is confusing, and the terminology is changed as suggested.

Reviewer 2 Report

Comments and Suggestions for Authors

In terms of the problem statement, the manuscript presents an interesting and well-established drawback of geometrical acoustic models. Indeed, the assumption that point sources can only be modeled with plane waves may have a significant effect on sound propagation, especially in the case of finite surfaces. Thus, the development of the presented model seems to be promising for room acoustics and performance halls. However, there are several issues with the paper that require improvements to make it scientifically valuable.

Firstly, the abstract should be rewritten to reflect the core objective of the paper. In this way, it will be possible to indicate the methodological framework used to address the problem and highlight the outcomes achieved. Currently, the novelty and significance of the study are not fully elaborated.

Secondly, it would be appropriate to enhance the introduction section. The authors should clearly explain what research gap their study attempts to fill, as well as elaborate on the limitations of the current methodologies. They should also state their objectives, novelty, and advantages over other existing models explicitly.

From a formal perspective, the referencing style should be revised. For instance, citations such as “Mechel [3] (pp. 513–666)” should be simplified to “Mechel [3]”, avoiding unnecessary details.

The mathematical expression in Section 2 is too difficult to understand. Each formula requires proper introduction, and all the variables should be carefully explained. It is recommended that all variables are presented in a clear list format, which will help readers understand the physical meaning and importance of each variable.

On another note, when using graphs (such as Figure 2 and other illustrations), the authors should provide a comprehensive explanation of how they were derived. If these are computer-simulated, then the exact methodology, assumptions, and parameters should be made clear. In general, the current validation process needs to be improved. For instance, a detailed explanation about the simulation design and validation criteria is highly desired.

It is important to compare the reflection from plane waves to those from spherical waves quantitatively. This is because the new method needs to be proven to be better than the traditional approach. Specifically, there should be discussion about the conditions (e.g., low frequency and grazing incidence) when both methods differ. This discussion would also help contextualize the trade-off between computational complexity and physical accuracy.

In addition to this, there is no adequate discussion about the computing setup employed for running simulations. It is important that a detailed description of the hardware and software utilized in conducting the experiment is presented by the authors. The computer hardware parameters, such as the processor speed, memory, GPU, and so forth, can be listed out in a table. As for the software part, it must be explained in detail.

Finally, a discussion section covering the possible application and future research opportunities should be included in the article. In particular, the authors have alluded to one possibility for employing the algorithm – in the performance spaces. This area requires further expansion; there are other possibilities for application of the method, such as designing acoustical properties of buildings or controlling outdoor noises. Future developments in the field can also be outlined.

Author Response

Firstly, the abstract should be rewritten to reflect the core objective of the paper. In this way, it will be possible to indicate the methodological framework used to address the problem and highlight the outcomes achieved. Currently, the novelty and significance of the study are not fully elaborated.
1. Reply: The abstract is rewritten as suggested.
Secondly, it would be appropriate to enhance the introduction section. The authors should clearly explain what research gap their study attempts to fill, as well as elaborate on the limitations of the current methodologies. They should also state their objectives, novelty, and advantages over other existing models explicitly.
1. Reply: The introduction has been extended and the novelty of the work is made clearer.
From a formal perspective, the referencing style should be revised. For instance, citations such as “Mechel [3] (pp. 513–666)” should be simplified to “Mechel [3]”, avoiding unnecessary details.
1. Reply: The referencing style is in accordance with the instructions given in the template for this journal.
The mathematical expression in Section 2 is too difficult to understand. Each formula requires proper introduction, and all the variables should be carefully explained. It is recommended that all variables are presented in a clear list format, which will help readers understand the physical meaning and importance of each variable.
1. Reply: All the variables are explained where they appear. A new Appendix B – List of variables has been added.
On another note, when using graphs (such as Figure 2 and other illustrations), the authors should provide a comprehensive explanation of how they were derived. If these are computer-simulated, then the exact methodology, assumptions, and parameters should be made clear. In general, the current validation process needs to be improved. For instance, a detailed explanation about the simulation design and validation criteria is highly desired.
1. Reply: All graphs and associated calculations are made with Excel using complex functions. This information is added to the text.
It is important to compare the reflection from plane waves to those from spherical waves quantitatively. This is because the new method needs to be proven to be better than the traditional approach. Specifically, there should be discussion about the conditions (e.g., low frequency and grazing incidence) when both methods differ. This discussion would also help contextualize the trade-off between computational complexity and physical accuracy.
1. Reply: The discussion of the results of the comparison in Figure 4 is extended. It must be concluded that there is no simple answer to the question, what is the difference in the result when the spherical wave reflection is applied instead of the plane wave approximation.
In addition to this, there is no adequate discussion about the computing setup employed for running simulations. It is important that a detailed description of the hardware and software utilized in conducting the experiment is presented by the authors. The computer hardware parameters, such as the processor speed, memory, GPU, and so forth, can be listed out in a table. As for the software part, it must be explained in detail.
1. Reply: All graphs and associated calculations are made with Excel using complex functions. This information is added to the text.
Finally, a discussion section covering the possible application and future research opportunities should be included in the article. In particular, the authors have alluded to one possibility for employing the algorithm – in the performance spaces. This area requires further expansion; there are other possibilities for application of the method, such as designing acoustical properties of buildings or controlling outdoor noises. Future developments in the field can also be outlined.
1. Reply: The discussion and conclusion sections have been extended as suggested.