Question

Given a container filled with identical objects, how could I find the number of objects in the container accurately purely by analyzing the sound produced on shaking? More specifically, which acoustic parameter should I focus on? Some ideas I have had so far are:

Looking at the number of amplitude spikes since the more objects there are, the more collisions there are

Using Fourier Transform to break down the combined sound into its constituent frequencies, finding the number of distinct frequencies. Unfortunately, I am not sure if the frequencies will be measured for each object, since the objects are identical
Options:

A) Counting the number of amplitude spikes as an indicator of collisions between objects.
B) Employing Fourier Transform to break down the sound into constituent frequencies and determining the number of distinct frequencies. Note: The objects are identical; unsure if distinct frequencies can be measured for each object.
C) Analyzing the sound's reverberation time within the container to estimate the number of objects.
D) Measuring the sound pressure level (SPL) changes within the container due to the number of objects present.

Answer 1

Determining the number of objects in a container by analyzing the sound involves physics concepts like reverberation time and SPL changes. Amplitude spikes and Fourier Transform might not provide accurate counts due to overlapping sounds and identical frequencies from identical objects.

Step-by-step explanation:

The task of determining the number of identical objects in a container by analyzing the sound produced on shaking involves a combination of physics concepts. While you may think of counting amplitude spikes as collisions occur, this method might not yield an accurate object count due to complex and overlapping sound waves. The use of Fourier Transform to analyze frequencies can be insightful, yet identical objects might not produce distinctly measurable frequencies when shaken together.

Instead, considering the reverberation time or the changes in sound pressure level (SPL) could be more effective. The reverberation time can give clues about how sound interacts with the objects in the container, while the SPL changes can indicate the presence of more objects absorbing or reflecting sound. However, measuring these parameters accurately necessitates a controlled environment and precise acoustical instruments. It's important to note that these methods may provide estimations rather than exact counts and generally require additional corroborative information.