Can One Hear the Shape of a Drum? [pdf](maa.org)
maa.org
Can One Hear the Shape of a Drum? [pdf]
https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/MarkKac.pdf
19 comments
Regarding realism, I wonder if it's possible to hear the difference between drums if you assume dampened vibration.
Interestingly, to me at least, I knew a local music store that made their own instruments for years, and had a kick drum shaped almost exactly like the one on page 1 of the pdf linked to (like a kidney bean). Of course, the head was ancient, as the creator had (IIRC) REMO put their heads on the hoops that he custom bent and sent to them.
Sounded different than a normal drum. Was pink sparkle coated, so perhaps that had something to do with it :)
The drum kit is still in the shop to this day (crazy old guy wants far too much for anything in the shop, as it has been there for an eternity, and well, all old is expensive, right?) I think about that set every now and then, as I myself was interested at one time.
Sounded different than a normal drum. Was pink sparkle coated, so perhaps that had something to do with it :)
The drum kit is still in the shop to this day (crazy old guy wants far too much for anything in the shop, as it has been there for an eternity, and well, all old is expensive, right?) I think about that set every now and then, as I myself was interested at one time.
You could look for an old Trixon drumset if you want an oddly-shaped bass drum:
https://www.trixondrums.de/trixon/trix249.htm
https://www.trixondrums.de/trixon/trix249.htm
I thought it would be a link to https://www.jstor.org/stable/29775597?seq=1.
I heard about this problem from David Webb (one of the people who found that the answer was no) back when I was a grad student at Dartmouth College.
I heard about this problem from David Webb (one of the people who found that the answer was no) back when I was a grad student at Dartmouth College.
Relatedly: Can one hear the fate of a coin? https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...
Reminds me of my time in music school. The ear training department had a special resident visiting that week and their skill was such that someone joked you could jingle the change in your pockets that person could tell you how much you had and in which denominations.
Related: can you hear the temperature of water?
https://m.youtube.com/watch?v=Ri_4dDvcZeM
Still unsolved for 2-manifolds embedded in 3D I believe.
You can’t hear the shape of a drum. But can you hear the shape of a cowbell?
You can’t hear the shape of a drum. But can you hear the shape of a cowbell?
You have to really explore the space.
Obligatory: https://youtu.be/bkJZbyrfx-Q
It’s really too bad that PBS canceled infinite series.
It’s really too bad that PBS canceled infinite series.
More recently Kelsey Houston-Edwards has been writing for Quanta: https://www.quantamagazine.org/authors/kelsey-houston-edward...
Cool, didn’t know that.
I also like how unrealistic the "drumheads" proposed in the proof were: https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum