The fundamental frequency of a vibrating string is directly related to its length. When a string of length 1.0m vibrates at a fundamental frequency of 256Hz, shortening the string to 0.4m increases the frequency. The new fundamental frequency can be calculated using the formula f = (n/2L)√(T/μ), where n is the harmonic number, L is the length of the string, T is the tension, and μ is the linear mass density. For the shortened string, the fundamental frequency is 640Hz.
PREREQUISITESPhysics students, music instrument makers, and anyone interested in the principles of wave mechanics and string vibrations.