Analytical Approximations for Sub Wavelength Sound Absorption by Porous Layers with Labyrinthine Slit Perforations
Round 1
Reviewer 1 Report
This interesting paper presents analytical approximations to compute the sound absorption coefficient, in either rigid or porous materials with slit perforation, using the equivalent fluid approach and the double porosity theory. The proposed method can be useful to investigate metamaterials. The paper is clear and well written. I just have a few comments, suggesting minor changes which I believe may be beneficial for the reader.
1) page 1 line 42: please specify that the plane wave impinges on the material at normal incidence.
2) page 2 line 47: for sake of clarity, H and V can also be reported in the caption of Figure 1, associated with pictures a) and b) respectively.
3) Figure 1 seems poor in resolution, some dimensions are difficult to read and seem stretched along one direction.
4) page 2, eq. 1 (optional): for a better readability, please consider to split this numbered equation as: eq. (1a) for THZ, eq. (1b) for THC, and eq. (2a) for TVZ; eq.(2b) for TVC.
5) page 2 eq. 3a: please specify that "i" is the imaginary unit.
6) page 2 eq. 3b: it is not clear what the variables ρBL and CBL represent. In fact, eq. 3a introduces ρL and CL
7) Please clarify if ΩS in eq. 3b to compute ZL, can either be ΩSH or ΩSV, as ΩB and T.
8) In my understanding, the model presented in section 2 assumes a rigid motionless frame. If this is the case, such assumption should explicitly be expressed.
9) page 3: eq. 6 seems like a sort of repetition of eq.s 5a and 5b. However, its purpose and the differences from eq 5 are not clear to me.
10) page 4: in my understanding, results presented in Figure 3 refers to a layer of mineral wool stacked on a layer of melamine foam. However, the thickness of each layer was not specified. Please, include these details in the manuscript, for example in Table 1.
11) page 4: in Table 1 the parameter Ωm is reported twice (in the second and last columns).
12) page 5: there is a typo in the caption of figure 4: (solid Lines)
13) In my opinion, it would be beneficial for the reader having a legend in some of the figures. Please, consider to add it to all the charts presented in this paper.
Author Response
1) page 1 line 42: please specify that the plane wave impinges on the material at normal incidence.
‘at normal incidence’ has replaced ‘incident’ in line 42
2) page 2 line 47: for sake of clarity, H and V can also be reported in the caption of Figure 1, associated with pictures a) and b) respectively.
The caption has been modified as suggested
3) Figure 1 seems poor in resolution, some dimensions are difficult to read and seem stretched along one direction.
The Figures have been replaced by higher resolution versions and augmented to indicate the relevant path length calculations
4) page 2, eq. 1 (optional): for a better readability, please consider to split this numbered equation as: eq. (1a) for THZ, eq. (1b) for THC, and eq. (2a) for TVZ; eq.(2b) for TVC.
The equations have been split as suggested
5) page 2 eq. 3a: please specify that "i" is the imaginary unit.
After equations (3a,b) is added ‘Time dependence is understood where ’.
6) page 2 eq. 3b: it is not clear what the variables ρBL and CBL represent. In fact, eq. 3a introduces ρL and CL
It is stated that and represent the complex density and compressibility of the rigid-porous matrix after equation (4)
7) Please clarify if ΩS in eq. 3b to compute ZL, can either be ΩSH or ΩSV, as ΩB and T.
Text amended to state is either or
8) In my understanding, the model presented in section 2 assumes a rigid motionless frame. If this is the case, such assumption should explicitly be expressed.
The rigid-porous assumption is stated in the Introduction
9) page 3: eq. 6 seems like a sort of repetition of eq.s 5a and 5b. However, its purpose and the differences from eq 5 are not clear to me.
Agreed. The text is amended to point out the different values of L and equation (6) is deleted.
10) page 4: in my understanding, results presented in Figure 3 refers to a layer of mineral wool stacked on a layer of melamine foam. However, the thickness of each layer was not specified. Please, include these details in the manuscript, for example in Table 1.
No. The rockwool and melamine foams are considered as forming individual porous layers. Amended text (line 101) states ‘rockwool or melamine foam’.
11) page 4: in Table 1 the parameter Ωm is reported twice (in the second and last columns).
The last column is deleted.
12) page 5: there is a typo in the caption of figure 4: (solid Lines)
corrected
13) In my opinion, it would be beneficial for the reader having a legend in some of the figures. Please, consider to add it to all the charts presented in this paper.
Explanatory keys have been added to all graphs
1) page 1 line 42: please specify that the plane wave impinges on the material at normal incidence.
‘at normal incidence’ has replaced ‘incident’ in line 42
2) page 2 line 47: for sake of clarity, H and V can also be reported in the caption of Figure 1, associated with pictures a) and b) respectively.
The caption has been modified as suggested
3) Figure 1 seems poor in resolution, some dimensions are difficult to read and seem stretched along one direction.
The Figures have been replaced by higher resolution versions and augmented to indicate the relevant path length calculations
4) page 2, eq. 1 (optional): for a better readability, please consider to split this numbered equation as: eq. (1a) for THZ, eq. (1b) for THC, and eq. (2a) for TVZ; eq.(2b) for TVC.
The equations have been split as suggested
5) page 2 eq. 3a: please specify that "i" is the imaginary unit.
After equations (3a,b) is added ‘Time dependence is understood where ’.
6) page 2 eq. 3b: it is not clear what the variables ρBL and CBL represent. In fact, eq. 3a introduces ρL and CL
It is stated that and represent the complex density and compressibility of the rigid-porous matrix after equation (4)
7) Please clarify if ΩS in eq. 3b to compute ZL, can either be ΩSH or ΩSV, as ΩB and T.
Text amended to state is either or
8) In my understanding, the model presented in section 2 assumes a rigid motionless frame. If this is the case, such assumption should explicitly be expressed.
The rigid-porous assumption is stated in the Introduction
9) page 3: eq. 6 seems like a sort of repetition of eq.s 5a and 5b. However, its purpose and the differences from eq 5 are not clear to me.
Agreed. The text is amended to point out the different values of L and equation (6) is deleted.
10) page 4: in my understanding, results presented in Figure 3 refers to a layer of mineral wool stacked on a layer of melamine foam. However, the thickness of each layer was not specified. Please, include these details in the manuscript, for example in Table 1.
No. The rockwool and melamine foams are considered as forming individual porous layers. Amended text (line 101) states ‘rockwool or melamine foam’.
11) page 4: in Table 1 the parameter Ωm is reported twice (in the second and last columns).
The last column is deleted.
12) page 5: there is a typo in the caption of figure 4: (solid Lines)
corrected
13) In my opinion, it would be beneficial for the reader having a legend in some of the figures. Please, consider to add it to all the charts presented in this paper.
Explanatory keys have been added to all graphs
Reviewer 2 Report
why do the simulations stop at 1000 Hz?
what are the practical applications?
Have acoustic measurements been carried out to verify the numerical models?
it is necessary to improve the caption of the figures, the trends to which geometry corresponds are not well understood
Author Response
why do the simulations stop at 1000 Hz?
The frequency range plotted in the Figures is restricted to below 1 kHz since the low frequency performance is of most interest.
what are the practical applications?
Additional text in the Introductions reads “Conventional means of improving the low frequency absorption by porous layers are to increase their thickness or to mount them with air spaces between them and a rigid backing surface. However, considerations of space and weight in aerospace or automotive applications may make such conventional solutions impractical.”
Have acoustic measurements been carried out to verify the numerical models?
No but the intention to make measurements to validate the presented predictions is mentioned in the Concluding Remarks.
it is necessary to improve the caption of the figures, the trends to which geometry corresponds are not well understood.
Captions have been amended and explanatory keys have been added to all graphs
