## 4 Discussion  
Even a preliminary analysis of the visualized data shows the convergence of the results obtained. A clearly observed fact is the low sound intensity visible on the XY plane in the region of the speaker centers (the color map of the sound intensity level in \(ZY\) plane indicates a high level at these locations), indicating that little energy is radiated in this plane, while most of the radiated energy from this area of the speaker can be seen on the \(ZY\) plane. More complex phenomena can be observed for frequencies lying near the limiting frequency of the loudspeaker crossover (around 2 kHz). The task of the crossover \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Freq**} & \multicolumn{2}{c}{**Mean Value**} & \multicolumn{2}{c}{**Standard**} & \multicolumn{2}{c}{**Mean Value**} & \multicolumn{1}{c}{**Standard**} \\  & **of Level Diff.** & **Deviation** & **of Level Diff.** & **Deviation** \\  & **XY Plane** & **XY Plane** & **ZY Plane** & **ZY Plane** \\ \hline
**[Hz]** & **[dB]** & **[dB]** & **[dB]** & **[dB]** \\ \hline
63 & \(-0.11\) & \(0.6\) & \(-0.01\) & \(0.3\) \\
125 & \(-1.7\) & \(0.6\) & \(-0.43\) & \(0.2\) \\
250 & \(-0.70\) & \(0.3\) & \(0.052\) & \(0.1\) \\
500 & \(-0.39\) & \(0.2\) & \(0.36\) & \(0.1\) \\
1000 & \(-0.65\) & \(0.2\) & \(0.078\) & \(0.4\) \\
2000 & \(-1.2\) & \(0.5\) & \(-0.68\) & \(0.1\) \\
4000 & \(-2.2\) & \(0.6\) & \(-1.5\) & \(0.3\) \\
8000 & \(-5.4\) & \(1.8\) & \(-5.3\) & \(1.9\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical measures of compared methods. Figure 7: Sound intensity vector fields in the \(ZY\) plane for the chosen one-third-octave frequency bands. Top row (REF)—intensity distribution for PU-method used as a reference. Mid row (NEW)—intensity distribution for proposed method. Bottom row—historgams of sound intensity level \(L_{I}\) difference between methods. is to accurately separate the signals in the frequency domain between the tweeter and woofer. Due to the finite attenuation of the crossover's low-pass and high-pass filters in this frequency range, both speakers emit signals that are usually phase-shifted, resulting in interference effects, and it can be observed as the formation of vortices in the sound intensity vector fields. The sound intensity distributions compared are very similar. Quantitative analysis shows that the differences in results for frequencies below 4 kHz do not exceed the measurement uncertainty guaranteed by the manufacturer of the PU probe, which is \(\pm\)1 dB for pressure and velocity sensors in frequency range from 40 Hz to 8000 Hz [13]. The increase in the average value of the difference observed for higher frequencies may be due to a systematic error associated with the fixed value of the distance between the measurement positions of the microphone (20 mm), which was not changed to ensure constant comparison conditions. However, the proposed method allows for freely reducing the sensor displacement step and adjusting the distance to the desired frequency range. On the other hand, for lower frequencies, the distance can be selected at the post-processing stage by selecting appropriate points from the measurement base (see Figure 4). As a great advantage of the proposed approach, it should be stated that only one standard microphone and a positioning system (by many users applied up to now only for pressure maps acquisition) were used to obtain visualization of the vector field of sound intensity, i.e., popular and relatively inexpensive tools (no need for specialized intensity probe used in this study only for reference). As another advantage of the proposed solution, the measurement time consumption of the proposed method is maintained at the level of the standard pressure distribution measurement. The number of measurement points is the same, and the resulting matrix with sound intensity vectors is reduced only by the two outermost rows and columns (\"perimeter\") of the original measurement grid (and matrix with pressure impulse responses).