# Directional Suppression of Monotone Noises with A Parametric Array Loudspeaker
## 4 Experimental Characterization of PAL's Pressure Field  
### Characterization of PAL's Directivity  
VCLs have a nearly omnidirectional directivity, while PALs can achieve a narrower directivity in the far field following the beam width defined by the ultrasound carrier wave [24; 29]. The PAL under test is shown in Figure 3a, which consists of 198 pieces of 40 kHz, 10 mm diameter, airborne ultrasound transducers (KS-A1040H07 CTR, Kessen, Guangdong, China) arranged in a hexagon-shaped array with an aperture size of 17 cm in diameter. Theoretically, the demodulated audio beam directivity \(D(\theta)\) can be predicted by the main lobe determined by the proposed array aperture of \(L\) and wave number of \(k\) as [34]  
\[D(\theta)=\mathrm{sinc}\,|\frac{kL\sin\theta}{2}|. \tag{11}\]  
To verify the PAL spatial characteristics, we measured the array far-field directivity at a distance of 1 m away from the aperture, using both the microphone and a calibrated sound level meter (AS844+, HIMA Instrument, Hong Kong, China) when the PAL is driven with a 1 kHz modulated continuous wave signal. The microphone senses pressure levels in the test field by recording peak-to-peak voltages, which are then converted into decibels (dBs) by post-processing. The sound level meter directly records the pressure levels in dB by A-weighting to simulate the human auditory characteristics. The measurement is conducted by mounting the test source on a rotary stage and manually rotating the source to record the data at every 5\({}^{\circ}\) step size. The comparison of the two measurement approaches is presented in Figure 3b, indicating that both measurement methods give a similar plot to clearly depict the PAL's far-field directivity, showing a \(-3\) dB main lobe width of around 40\({}^{\circ}\). The form factor of the adopted PAL also gives rise to two grating lobes at \(\pm 30^{\circ}\) with lower amplitudes compared with the main lobe [24; 34].  
The directivities of the PAL with an aperture size of 17 cm and a generic VCL with a sound emitting surface area of 85 mm \(\times\) 70 mm are measured with the sound level meter at the same 100 cm distance when both emitting a 1 kHz signal. The comparison is shown in Figure 3c by plotting both directivity maps with the normalized amplitude (n.a.). The VCL presents a wide directivity that is close to an omnidirectional pattern, with a \(-3\) dB beam width of around 110\({}^{\circ}\), while the PAL's \(-3\) dB beam width is reduced to around 40\({}^{\circ}\) by considering the main lobes. Hence, for the current aperture design shown in Figure 3a, as the secondary source, the PAL can reduce the effective beam width by 64% of that of the conventional loudspeaker to provide much more directional ANC effects.  
Figure 3d further compares the directivity pattern of beams projected from the PAL when the carrier waves are modulated with different audio frequencies. For verification purposes, the test frequencies are selected from low to high at 250 Hz, 1 kHz, and 4 kHz, within the transducer's \(-6\) dB bandwidth of around 3 kHz. The results demonstrate similar beam directivity patterns when the PAL is driven with signals modulated with either low or high audio frequencies. This further verifies the feasibility of using the PAL to tackle different monotone noises.