Скачать с ютуб The Musical Instrument Unlike All Others в хорошем качестве

The Musical Instrument Unlike All Others

The musical saw is really weird. It makes beautiful, haunting melodies, while simultaneously raising even more perplexing questions about the mathematics and physics of how it works. In this video, we take an exploratory approach to answer many questions, converging to two main queries: First, why can I change the pitch of the musical note on a saw just by bending it; and secondly, how can it vibrate and sing for so long when it is held in my hands, and should be muted? By approaching these questions with both theory and experiment, we end up gaining a deeper understanding about a wide swath of technical concepts, such as the harmonic oscillator, Lagrangian mechanics, and material science, and in the end, we discover that the saw ties two seemingly unrelated areas and concepts together: namely an indispensable theoretical tool used in quantum mechanics, as well as the concept of Gaussian curvature in the differential geometry of surfaces. This is my submission for #some3. 00:00 - Introduction 01:00 - Motivation: How do Instruments make sound? 02:44 - Springs: Learning by Analogy 03:08 - Continuous Media: Everything's a Spring! 04:10 - Newton vs. Lagrange: Minimal Physics 06:15 - Frequency from Stiffness: The Intuition 07:35 - Visualizing the Vibrations: A Thought Experiment 11:56 - Redistributing the Slack: Nature's Cheat 12:29 - Clues from Experiment: Pouring Salt on the Saw 15:01 - Gaussian Curvature: Why Bending is Costly 17:21 - Forbidden Modes: Dispersion, Wavenumber and Frequency 21:45 - The Magic of the 'S': Evanescence and WKB Theory 24:57 - Summary