Simulation Of Transmitters and Phase Delay Calculations

Pardon me , sir for keeping you in the dark for all this time but i needed to get something conclusive before submitting the results. I have completed coding the simulation for the ultrasonic transmitters which is also capable of calculating the phase delay for n number of transmitters (as of now limited to linear ,array not yet implemented) and also capable of transmitting this data to an arduino(still have to figure out the character encoding and flushing the serial buffer but the code is complete). The link to the code is https://github.com/1sand0s/Inter_Haptics/tree/master/IS_UltraSonic/src/IS_UltraSonic.

The link to the video showing the implementation is below:-
https://youtu.be/lzrv-VvoatU

As shown in the diagram , in order to change the directivity or the angle of the principle maximum ,the transmitters are excited at different instances thereby causing constructive interference at different points and hence changing the orientation of the maximum. Lx is the distance from the transmitter at nth position to the focal point and R is the distance from the central transmitter , so Lx is compared with R and the transmitter is either set back or advanced by a factor ((mod(Lx-R))/speed) and this phase delay results in a constructive interference at the desired point.

Material Read In First Week Of June

Through the various papers referred , i have inferred the following points

Transmission: 
 As specified before , i intended to use the 40khz ultrasonic transmitter  from murata-MA40S4S 
 (i have ordered in bulk after it perfectly suited the need for the project with the favorable directivity and sound pressure level) .For the sake of clarity i recapitulate ,they basically contain quartz crystals which undergo deformation upon application of an AC wave and if the frequency of the applied AC wave coincides with the resonant frequency of the crystal ,the amplitude of the output mechanical disturbance(ultrasonic wave) is maximum .However tiny receptors embedded in our skin called mechanoreceptors

are incapable of detecting vibrations at a frequency of 40khz, it is most sensitive in the frequency range

Therefore i plan to modulate the AC 40khz sinusoid with the amplitude of a 100-200 Hz sinusoid and hence creating a multi-frequency wave which is then amplified to 15Vp-p and fed to the transmitter

Focal Points
This is what i am focusing right now on, reading up material on phase-plane and basically try to correlate the points of constructive interference to the phase differences of the transmitter to form the focal point and eliminate the background noise