Michal Demeter Tvrdoň

Can You Hear the Shape of a Drum?

Around half a century ago, the Polish-American mathematician Marek Kac posed a rather intriguing question: Can you determine the shape of a drum by listening to its sound? Surprisingly, it took a while before we could answer this question, and partially thanks to Dartmouth, we know the answer.  

Let me explain: every musical instrument can play certain tones with different pitches, where the pitch corresponds to the first harmonic. However, the first harmonic isn't the only frequency the instrument produces. Second and "n" other harmonics arise based on the instrument's geometry. 

This naturally leads us to question whether we can deduce the instrument's shape based on the sounds it produces. Carolyn Gordon and David Webb, both esteemed mathematics professors at Dartmouth, tackled this fascinating inquiry. Their remarkable work established that different shapes could produce identical harmonics, unraveling a great mystery in the process.

I would go down the rabbit hole of what math they used, but at this moment, I have no idea how. However, I can promise you that in the next four years, I will write an explanatory blog post. Today, I would rather focus on Professor Miles Blencowe.

If it weren't for Professor Blencowe, I might never have encountered this thought-provoking question. At some point during the stressful pursuit of high school accolades, I lost my passion for comprehending the world. My priorities shifted from gaining knowledge for its own sake to chasing 1s in the Slovakia educational system and 7s in the IB program in Tanzania. To be honest, this shift led me to resent the idea of entering college at the start.

But things took a turn for the better. I'm not entirely sure if it was the Dartmouth Outing Club trips, on average pretty cool classmates, the small class sizes, or the great mental health support system, but the specifics don't matter as much as the overall transformation. Suddenly, I started feeling safe and began immersing myself in exploring the world, both inside and outside the classroom.

Miles, who graciously allowed us to call him by his first name, played a significant role in this transformation. Instead of rushing through the syllabus, he guided us through the captivating world of physics. Over the past eight weeks, I began grasping concepts in special relativity and quantum mechanics, and I even received an introduction to partial derivatives and the Fourier series.

Miles is also the one who introduced the question, "Can you hear the shape of a drum?" While this question might not have been part of the official curriculum, it encouraged me to dedicate extra hours to understanding how sound and waves are generated.

When I first arrived at Dartmouth, I initially aimed to survive four years of engineering and complete my distributive requirements. However, my perspective has changed, and I now eagerly anticipate my future courses. No matter the field you study, having a more diverse background always helps in one way or another. It took me a while to figure it out, but now I realize that many of the problems we are facing now as a society result from people getting too narrowly focused on education resolution in a skewed worldview. It took me a while to realize this, but I now understand that many of society's problems stem from people pursuing overly narrow educational paths not as applicable in the increasingly complex world.

In conclusion, Professor Miles Blencowe is an exceptional teacher. If you ever have the opportunity to take a class with him, I highly recommend it.

Some of Professor Blencowes work: A Quantum Soundscape