Add new comment

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.
Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!
How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?
Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.
PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
The corner is not PERFECTLY sharp, of course, on a real string, but it really is a long way from being a sine wave. As you say, bending stiffness of the string stops it having an ideally sharp corner. But there are plenty of measurements of real bowed strings vibrating, and also highspeed videos showing the Helmholtz motion directly.
The motion of a bowed string brings in different physics from the vibration of a plucked string such as a guitar. When you pluck a string you certainly excite many overtones of the string, and these are roughly harmonically spaced, but they each vibrate independently of each other: a characteristic of linear systems. But when you bow a string carefully and steadily the nonlinear interaction with friction at the bow produces a periodic motion consisting of exact harmonics, even though these will not precisely match the natural overtone frequencies of the string. The motion has been analysed quite extensively, and it tells you things about how a player might be able to vary the tone of a note, and how a stringmaker might design strings to produce different balances of sound.