# The Sonic Resonance Method and the Impulse Excitation Technique: A Comparison Study
## 3 Results  
Because the material, dimensions, mass, and intrinsic properties of the sample were the same for both methods, SRM and IET, only resonant frequencies obtained by SRM and IET could be different. Therefore, only these frequencies were taken into account for the comparison of SRM and IET. The results obtained by the SRM and IET are shown in Table 2. The resonant frequency of each sample (listed in Table 1) was measured 12 times with both methods and the mean values and standard deviations were calculated. The relative differences between the mean values of the resonant frequencies \(f_{IET}\) and \(f_{SRM}\), were calculated according to the equation:  
\[\frac{\Delta f}{f_{m}}=\frac{2(f_{SRM}-f_{IET})}{f_{SRM}+f_{IET}}. \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Sample** & \multirow{2}{*}{**Method**} & **Resonant** & **Standard** & **Relative Difference** & \multirow{2}{*}{**\(t\)-Test Score**} & **F-Test Score** \\ \cline{3-3}  & **Material** & & **Frequency [Hz]** & **Deviation [Hz]** & & & & \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{Aluminum} & SRM & 4381.75 & 3.7444 & \multirow{2}{*}{\(-0.00029\)} & \multirow{2}{*}{0.88} & \multirow{2}{*}{1.38} \\ \cline{3-3}  & & IET & 4383.00 & 3.1856 & & & & \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{Stainless steel} & SRM & 3068.05 & 2.3448 & \multirow{2}{*}{\(-0.00003\)} & \multirow{2}{*}{0.10} & \multirow{2}{*}{1.19} \\ \cline{3-3}  & & IET & 3068.15 & 2.5589 & & & \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{Carbon steel} & SRM & 1553.85 & 35.0418 & \multirow{2}{*}{0.00158} & \multirow{2}{*}{0.16} & \multirow{2}{*}{1.32} \\ \cline{3-3}  & & IET & 1551.39 & 40.2075 & & & \\ \hline \multirow{2}{*}{4} & \multirow{2}{*}{Kaolin ceramics 1} & SRM & 3374.54 & 82.9955 & \multirow{2}{*}{0.00562} & \multirow{2}{*}{0.53} & \multirow{2}{*}{1.22} \\ \cline{3-3}  & & IET & 3355.64 & 91.7184 & & & \\ \hline \multirow{2}{*}{5} & \multirow{2}{*}{Kaolin ceramics 2} & SRM & 3421.60 & 10.6667 & \multirow{2}{*}{\(-0.00050\)} & \multirow{2}{*}{0.38} & \multirow{2}{*}{1.16} \\ \cline{3-3}  & & IET & 3423.31 & 11.4891 & & & \\ \hline \multirow{2}{*}{6} & \multirow{2}{*}{Alumina porcelain} & SRM & 2952.85 & 144.0841 & \multirow{2}{*}{\(-0.00023\)} & \multirow{2}{*}{0.01} & \multirow{2}{*}{1.03} \\ \cline{3-3}  & & IET & 2953.52 & 141.7116 & & & \\ \hline \multirow{2}{*}{7} & \multirow{2}{*}{Soda-lime glass} & SRM & 2372.19 & 9.3747 & \multirow{2}{*}{\(-0.00011\)} & \multirow{2}{*}{0.06} & \multirow{2}{*}{1.22} \\ \cline{3-3}  & & IET & 2372.45 & 10.3524 & & & \\ \hline \multirow{2}{*}{8} & \multirow{2}{*}{Corundum ceramics} & SRM & 1813.70 & 4.2823 & \multirow{2}{*}{0.00006} & \multirow{2}{*}{0.06} & \multirow{2}{*}{1.10} \\ \cline{3-3}  & & IET & 1813.59 & 4.4912 & & & \\ \hline \multirow{2}{*}{9} & \multirow{2}{*}{Silicon carbide} & SRM & 2932.75 & 3.9341 & \multirow{2}{*}{0.00050} & \multirow{2}{*}{1.05} & \multirow{2}{*}{1.91} \\ \cline{3-3}  & & IET & 2931.28 & 2.8493 & & & \\ \hline \hline \end{tabular}  
* \({}^{1}\) Ceramics based on Sedlec kaolin fired at 1150 \({}^{\circ}\)C. 2 Ceramics based on Kemmiltz kaolin fired at 1150 \({}^{\circ}\)C.  
\end{table} 
Table 2: Resonant frequency measured using SRM and IET method. Figure 2: IET apparatus (1—microphone, 2—preamplifier, 3—personal computer, 4—sample, 5—hammer). Table 2 shows that this difference is low, mostly less than 0.05%, and the highest value of 0.56% was valid for kaolin ceramics. These small differences suggest good agreement between IET and SRM results. To obtain more reliable information, a t-test (see e.g., [25; 26]) was performed to compare mean values. The number of samples was \(n_{SRM}=n_{IET}=n=12\). The degrees of freedom \(k=n_{SRM}+n_{IET}-2=22\) and the critical test score \(t_{crit}=2.07\) for the significance level \(\alpha=0.05\) were the same for every comparison.