This question is part of the International Physics Tournament 2023. The entire problem statement reads : How accurately can you determine the number of matchsticks in a matchbox from the sound it makes when you shake it ? Can the same methods be applied to a box containing chewing gums ?
I, along with my friends have tried to solve this problem. our partial solution
Since the question also asks if the same methods can be applied to a box containing chewing gums, we have tried to model our solution indpendent of the shape of the matchstick. Does our approach make any sense ? Is there a means to theoretically determine the accuracy of measurments without any experiment, via dimensional analysis for instance ?
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Sriram S
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3I doubt there is a way to do this that does not rely on experiment. For a very similar problem see: Can I compute the mass of a coin based on the sound of its fall? – John Rennie Apr 14 '23 at 05:19
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No offense to the folks who are making these questions up, but an AI algorithm can probably be trained to differentiate these sounds quite well... and absolutely nobody would have any idea how it does that. This ain't physics. This is practical engineering, at best. It is an interesting class of problems, but I wouldn't ask them as part of a physics contest. – FlatterMann Jan 22 '24 at 06:39
2 Answers
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If you have one matchstick in a matchbox, you have a weak sound with small amplitude and higher frequency. A single matchstick does not have enough mass to impart enough energy into the side of the box to make the side of the box deflect very far, thus giving a higher frequency and lower amplitude volume. (high freq, lower volume amplitude)
On the other hand, if you have many matchsticks in a matchbox, you have a strong sound with high amplitude and lower frequency. Many matchsticks have enough "additive mass" to impart enough energy into the side of the box to make the side deflect further out, thus giving a lower frequency, and higher amplitude in volume. (lower freq, higher volume amplitude)
So in summary, more matchsticks is proportional to lower frequency and higher volume amplitude.
Things to consider: Each matchstick should be of the same length and same mass for the above conjecture to be true.
steveK
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The box of matches can be completely full (matches fit snugly in the box), completely empty, or somewhere in between. Using sound alone, how accurate can the number of matches in the box can be estimated?
Using sound alone, I can't distinguish between a full and empty box because neither makes a sound when shaken. The full box of matches (snugly packed) will act like a solid object.
So in the case of empty and full boxes, the method is completely unreliable and these are the two simplest cases. It does not bode well for a solution to partially filled boxes.
The only solution involves stretching the definition of shake. If the matchbox can be dropped from a given height (and still be able for the matchbox to land flat. Then the initial sound made on impact would be proportional to the total mass of the matchbox including matches.
With the mass of the empty box and the mass of each identical matchstick, one can compute the number of matches in the box. This will be far more accurate then trying to deduce the number of matches by analyzing the white noise generated by shaking the box continuously.
Stevan V. Saban
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