FYKOS Year 36 Series 5 Problem 1 — flageolet under pressure · FYKOS 36 #36.5.1
Physics · mechanics · optics
Problem
Vojta plays the cello. He lightly places his finger on a string, tuned to the frequency f, at a distance of 1/n of its length from the head of the instrument and sounds it, hearing a tone of fundamental frequency f1. He then presses the string fully against the fingerboard at the same point and sounds it again. This time the instrument produces a tone of fundamental frequency f2. Determine the ratio of the frequencies f1/f2 as a function of the natural number n.