Take a box (e.g. a matchbox), filled with identical objects (e.g.matches, balls, …). Find a method to determine the number of objects in the box solely by the sound produced while shaking the box. How does the accuracy depend on the properties of the objects, the box, and the packing density? 

Is it possible to use a AI model to analyze the sound? If yes, How?

very badly posed question.

Of course it depends on the properties of the objects in the box.

What if they are a lite -weight sponge, and make no noise ?
What if they are a compound object, like 'nested' balls, that make multiple sounds on collision ?

the hardest part of finding an answer is making sure you ask the right question.
And you can call it AI modelling, but it's still a computer, so the old adage still applies; "garbage in, garbage out".

If the objects are air molecules, the answer is clearly "no".
As MigL has pointed out, the question needs work.

The question is copied from https://www.iypt.org/problems/, @flyer6 can you be more specific regarding your interest in the competition?