In their revised manuscript, authors meticulously addressed each comment and concerns point-by-point. Overall, their answers are both clear and precise enough and improved the manuscript reading and full understanding of the protocol.
Some last comments are proposed for further discussion.
 
- I suggest authors to indicate when needed the type of exercise they manipulate, rather to state “exercise protocol”. As such, constant workload exercise at 5% above VT1 is preferred, and has to be written when appropriate. 
Note that with reference to the physiological events of VT1, the true and exact measurements come from gas exchange measurement, even they can be identified indirectly by means of HRV. For sure, HRV could be a reliable, non-invasive, and low-cost method of assessing VT1 (and VT2). 
 
-VO2max criteria/exhaustion assesment: references included in Supplementary File 2 did not assess VO2max according to usual criteria (see Taylor et al., 1955) encountered in exercise physiology.
It is likely that end point of exercise (voluntary exhaustion) will differ according to the profile of the subjects. Do you expect to provide verbal encouragement, ask RPE score?
 
-Authors replied that VT1 is the exercise intensity (i.e., power output, cycling ergometer) to maintain (start point of exercise protocol) and that will soon drift to RCP and beyond, towards volitional exhaustion. Here, there is an issue! We know in exercise physiology that VO2 steady state at or slightly above 5%) VT1 can be maintained for a while; the slow drift you reported occurs at or above VT2 (see the extensive research work of Jones, Poole and co-authors on the VO2 kinetics during constant work rate exercise. Maintaining power output at VT1 is belonging to the moderate exercise domain, without important drift in any physiological variables (respiratory, cardiac, muscle..) except after more than 20-25 minutes, especially in Lab settings without cooling effect. In this case, a drift in HR (maybe HRV) can occur due to different underlying origins (e.g., heat-induced hypervolemia, passive-heat stress increases heart rate), such as blood flow redistribution among tissue that can affect cerebral oxygenation. It means that authors should report respiratory rate and heart rate time course as suggested, and verified the changes over time in these two variables with respect to the cerebral oxygenation response. Note that minute ventilation and cardiac output are more robust and complete (volume x rate changes) into the cardiorespiratory monitoring.
 
-Competing hypothesis not to rule out.
With exhaustion, whatever the exercise protocol (incremental, constant work, rate), reduced CO2 levels may occur and result in vasoconstriction and reduced cerebral blood flow, and so in NIRS-parameters (O2Hb). 
 

Thank you for addressing all my concerns in detail, they are sufficiently addressed now. Only the sampling plan requires in my view further clarification and possibly a revision:

4) The sampling plan describes a smallest telescope approach to establish a SESOI, which I
think is a val appoach given the risk for bias and the challenge in establishing a mechanistic
SESOI. yet, sample size estimates seem based on effect size estimates in previous literature.
Could the authors please clarify? Further, given their design, I am wondering whether (nested)
Bayesian hypothesis testing may be more sensitive and robust, as it provides flexible stopping
options?
Response authors: To justify our sample size, we decided to rely on statistical power, namely the
probability of detecting an effect (i.e., not accepting the null hypothesis) provided that this
effect exists. The sample size computation was not performed using the SESOI because the
latter corresponds to the effect size that an earlier similar study would have had 33% power to
detect. However, for a sample size justification, we want the power to be fixed at 80%, which
corresponds to a β level of .20. We made this choice in a way that the Type I error is four
times less likely to occur than the Type II error (see Cohen, 1988). The expected effect size
was estimated from previous similar studies in terms of variables of interest and experimental
design, as recommended by Lakens (2022).

- Thank you for the explanation. It is, however, not in line with what is stated in manuscript, which includes a power calculation for 90% (which is the PCI RR requirement). Also the explanation of the sampling plan in the manuscript is not very clear "The small telescopes approach was used to determine the smallest effect size of interest (SESOI; i.e., the difference that is considered too small to be meaningful;
Simonsohn, 2015). Accordingly, the SESOI was set to the effect size that an earlier
study would have had 33% power to detect (Lakens et al., 2018).". Please explain the telescope approach and why the SESOI was set to effect size that an ealier study would have had 33% power to detect it. What is the value for this effect size?

Table 1 lists the mapping of hypotheses to the sampling plan. Some assumed effect sizes are unbeliably large (>1.3) and it not clear where these values stem from. As a general point, it is also very questionable to base the sampling plan on previous effect size estimates from literature that was not preregistered. Simulations and meta-analyses suggest that on average non-preregistered literature (that may be subject to all forms of biases) yields effect size that 2-3 times larger compared to preregistered work (https://journals.physiology.org/doi/full/10.1152/jn.00765.2017; https://www.frontiersin.org/articles/10.3389/fpsyg.2019.00813/full; https://www.nature.com/articles/s41562-019-0787-z). Please clarify this point and consider revising the sampling plan accordingly.

Cerebral mechanisms underlying the effects of auditory stimuli during submaximal exercise
 
 This study aims to determine how the point of onset of cerebral oxygenation decline during an incremental exercise protocol is modulated by an auditory stimulus (i.e., music). Three conditions were compared: asynchronous music, audiobook control, and no-audio control. During the cycling task (a constant work rate exercise protocol), brain oxygenation will be recorded using a continuous-wave fNIRS system. Medial and dorsolateral prefrontal cortex (PFC), primary motor cortex and lateral parietal cortex will be measured over the two cortices.
 
Title: Cerebral oxygenation or correlates should be used in the title. But not cerebral mechanisms that were not assessed per se.
 
Overall, objective and hypotheses are clearly exposed and based on a strong scientific background. However, there are some potential concerns to tackle.
Introduction as a whole is quite long; the two first pages (up line 80) could be synthesized in order to move quickly on the main topic delivered by this original investigation. 
From line 108, lines 124-126, regarding fNIRS studies during incremental (upright) cycling exercise, some first relevant studies that showed the typically curve of brain oxygenation over the PFC are lacking (doi: 10.1016/j.resp.2006.08.009 and doi: 10.1007/s00421-007-0568-7). Note that brain deoxygenation occurs after the second ventilatory threshold. There are plenty of research works during cycling incremental exercise with fNIRS mainly over the PFC. Regarding a submaximal exercise at a constant power output, the brain deoxygenation is not so referenced and likely does not occur each time. Please clarify / comment on the real possibility to observe a deoxygenation pattern during submaximal constant exercise.
L 98. “Recently”. First studies that have measured brain oxygenation (and not metabolism) were proposed about 15-20 years ago.
L 101. Replace “tool” by “technique” or “method”
L 105. What is referring to “Exercise metabolism”? through oxygen consumption measurement?
Up to 10 Hz: fNIRS device for a while can sample up to 50 Hz.
L 130. Previous references (see above) have showed this idea, as indicated in a first review on the topic of fNIRS during incremental exercise where brain deoxygenation phenomenon was presented (doi: 10.1016/j.ymeth.2008.04.005.).
L 120-130. This section is quite important in the rationale of the present study. They are several hypotheses explaining the possible deoxygenation occurrence at such exercise intensities that were proposed in the three doi references above and in Rooks et al. (2011) but for incremental exercise test only.
 
L168-175. These tests are precious. It is a shame that non-cortical haemodynamics variables will be not considered as proposed by the current guidelines; even if the exercise (physiological) load (power output in watts) is judged similar, the conditions could modulate affective response (emotional states) and so autonomic nervous system accordingly. This in turn may change the brain oxygenation patterns. It is suggested to implement the autonomic nervous activity assessment during the three conditions as more control.
 
Regarding the methods, they are well presented and appear suitable for testing the hypotheses.
L219. What is the exact incremental protocol test for determining VO2max? What are the criteria for selecting VO2max values?
L220. Based on a typical incremental VO2max test, ventilatory thresholds can be determined accurately, mainly VT2, with the help of gas respiratory exchanges.
Concerning the hypothesis on the decrease of brain oxygenation during incremental test, literature showed extensively that this phenomenon occurred around VT2. It is unclear why VT1 is here targeted.
L 222. It is not clear also and surprising to use the heart rate to setup 5% above VT1 in terms of exercise intensity. Please comment on this choice as compared to power output
L241. 63 rpm is selected as a criterion. It is surprising and not argued.
Overall, the exercise protocol testing is unusual in the field of exercise physiology and does not seem the best one for showing brain deoxygenation. It becomes confusing sometimes when exercise term is cited. Brain deoxygenation occurence and its determinants are different across the type of exercise protocol (incremental vs. constant).
 
L255. Cardiorespiratory. This is inexact. Only cardiac activity was used here. Again, respiratory measurements are lacking. They are required for determining the exercise intensity domains (see doi: 10.14814/phy2.14098).
L322. Low pass filter of 0.1 Hz is often required (doi: 10.1117/1.NPh.4.4.041403)

I congratulate the authors on this carefully designed fNIRS study to investigate cerebral mechanisms underlying the effects of auditory stimulation during exercise on psychological wellbeing.

The submitted report provides in many aspects a detailed description of the methology, the sampling plan and the analysis plan. To provide a more concise overview, I would kindly ask the authors to submit the Preregistration for fNIRS" template that was recently developed (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9993433/#r55; https://osf.io/hb4um/).

Further, I have the following requests for clarification and suggestions with regards to the planned methodology:

1) It appears from the manuscript that the fNIRS device does not use short-separation channels that are considered state-of-the-art to account for extracerebral noise: https://www.spiedigitallibrary.org/journals/neurophotonics/volume-10/issue-1/013503/Performance-comparison-of-systemic-activity-correction-in-functional-near-infrared/10.1117/1.NPh.10.1.013503.full
In fact, extracerebral noise is not mentioned as a confounding factor in the protocol. Please clarify how you intend to correct for it, also given that it can strongly bias results with false positive findings for oxygenated Hb in particular (see reference above). This point is also highly relevant in the context of exercise, which can further confound fNIRS result in the form of an increase in extracerabal oxygenated Hb (see for details here: https://www.sciencedirect.com/science/article/pii/S1053811923000290).

2) The protocol mentions that a substantial part of the data will be contiminated by motion artefacts. It is quite likely that significant proportions of data for some subjects may not be usable. The protocol should include clear data exclusion criteria with regards to motion an other aspects and describe how it is ascertained that the target sample size will be achieved.

3) To establish good quality for data, I would stongly suggest using the qt-nirs toolbox: https://github.com/lpollonini/qt-nirs

4) The sampling plan describes a smallest telescope approach to establish a SESOI, which I think is a val appoach given the risk for bias and the challenge in establishing a mechanistic SESOI. yet, sample size estimates seem based on effect size estimates in previous literature. Could the authors please clarify? Further, given their design, I am wondering whether (nested) Bayesian hypothesis testing may be more sensitive and robust, as it provides flexible stopping options?