Effect of acoustic wave striking an object

Question

I am trying to understand the effect an acoustic wave has on an object. I have two speakers, one on top of another, and both emitting a Sine wave of 64Hz generated in MATLAB sampled at 44100. I place a sheet of paper at a distance 'd' in front of the paper. I then observe the vibrations on the paper using a Dynamic vision sensor(DVS) based event-based camera which can capture changes in intensity at every pixel with very high resolution(in the order of microseconds). So this means when the paper vibrates, I will have the paper's pixel locations and their timestamps(when the paper moves). The entire setup is as shown in the figure below(this is what the camera sees -the side views of the paper and the speaker)image of the left is the camera's the theoretical view and image on the right is an actual frame that the camera sees:

I am trying to understand the time of arrival of the acoustic wave on the surface of the paper.

1. From the event camera's data, I observe vibrations at different time stamps at different positions on the paper. How do I theoretically predict and understand the different time instances at which the sound wave would strike different parts of the paper?

2. Would it be possible to calculate the approximate distance between the speaker and paper using d=c*t where c is the speed of sound in air and t=tp-ts where tp = time at which wave hits the paper and ts = time at which wave was emitted from the speaker?

3. Would I be able to achieve 2) better if I placed one speaker facing the center of the paper?

I would appreciate any tips, pointers or resources to understand acoustic wave propagation.

Answer 1

The short answer is that yes, you can use the simple distance and speed values as you describe, to get a crude estimate. Bear in mind that a peak pressure on the paper corresponds to a peak movement of air but a peak acceleration of the paper.

If you wanted greater accuracy then you would need to characterise the radiation pattern of the speaker. Typically this will be spherical, centered on the base of the bass driver (as you say that frequencies handled by the tweeter are not detectable). You could then model how the wavefront propagates across the gap and impacts the paper. But I am doubtful that your sensor arrangement will have enough resolution to pick up the very small phase differences which will occur at 64 Hz (wavelength about 5 m), over the short distances involved.