## 5 Discussion  
### Accuracy and Consistency of Results  
The primary objective of this study was to employ smartphone audio recording as a means to determine \(g\) via the free fall method, aiming for accuracy and reliability comparable to established reference values. The calculated value of \(g\) from our experimental setup, accounting for associated uncertainties, yielded a precise measurement of 9.8274 \(\pm\) 0.01 m/s\({}^{2}\). Notably, this value demonstrated a remarkable alignment with the locally accepted reference value. The acceleration due to gravity by an altitude calculator  
Figure 5: Correlation between T\({}_{\text{theory}}\) and T\({}_{\text{experiment}}\) (**a**) and T\({}^{2}\) and H (**b**).  
estimates the approximate acceleration due to gravity on the surface of the Earth based on the altitude [40]. The equation for the acceleration due to gravity based on altitude is:  
\[g_{alt}=g\times\left(\frac{r_{e}}{r_{e}+h}\right)^{2} \tag{8}\]  
where \(h\) is the altitude above mean sea level (AMSL), \(g_{alt}\) is the acceleration due to gravity at a specific altitude, \(r_{e}\) is the mean radius of the Earth (6371.009 km), and \(g\) is the acceleration due to gravity at sea level (9.80665 m/s\({}^{2}\)) [41]. To measure the height of the experimental location, it was found that the altitude above mean sea level was 176 m. When calculated using Equation (8), we obtained \(g_{alt}\) is 9.80611 m/s\({}^{2}\). This was found to be close to the nominal \"average\" value at the Earth's surface, known as standard gravity, which is, by definition, 9.80665 m/s\({}^{2}\)[41], which results in a minimal relative error of 0.0055%. A review of research articles and textbooks revealed that the standard reference \(g\) value is 9.81 m/s\({}^{2}\)[8; 9; 10; 11; 12; 21; 25]. The congruence between our calculated \(g\) and the established \(g\) value near the Earth's surface, which stands at approximately 9.81 m/s\({}^{2}\), and the experimental location is 9.80611 m/s\({}^{2}\), and the methodology presented here yielded results within accuracy levels of 99.8226% and 99.7829%, respectively. This underscores the accuracy achieved through the utilization of smartphone audio recording, despite inherent challenges in precise time measurement at sub-second scales, with the smallest relative error amounting to 3.27%. This small margin of error is indicative of the reliability and precision of the experimental setup. The consistency of our results was evident through systematic experimentation, varying the release heights of the steel ball in controlled increments. Through meticulous data collection and averaging procedures, the time measurements acquired via audio recording consistently aligned with theoretical calculations. The comparison between theoretical and experimental time measurements provides strong evidence of a high degree of correlation, further supporting the accuracy of the obtained results across varying experimental conditions. Moreover, the propagated uncertainty of \(\pm\)0.01 emphasizes the precision achieved using smartphones for time interval measurements pertinent to gravitational experiments. This level of precision is notable considering the simplicity and accessibility of the method, underscoring the potential of smartphone technology in facilitating accurate scientific measurements. The above discussion clearly shows that the results obtained through smartphone audio recording demonstrated not only accuracy but also commendable consistency in determining gravitational acceleration via the free fall method. These findings validate the feasibility and reliability of utilizing smartphone onboard microphones as a convenient and precise tool in experimental physics, particularly in educational settings aiming to enhance students' understanding of fundamental physical principles.