On the phenomenon of natural-frequency splitting of a guitar string caused by a magnetic field

Abstract

A magnet can affect the vibration of the metal strings in a musical instrument. We show that the magnetic field from a magnetic pickup can cause a frequency splitting of a metal guitar string’s normally degenerate transverse vibration modes, leading to a beat note in the resulting sound. The amount of frequency splitting induced by the magnet depends on the product of the induced magnetization in the ferromagnetic string, and the magnet’s spatial gradient at the position of the string, and is on the order of a few Hz. We apply free vibration theory to the string to obtain an eigenvalue problem, which we solve using a distributed-transfer function method. This method accurately predicts the natural frequencies of the vibrating guitar string in a non-uniform magnetic field. Videos of a high-E string vibrating with and without a nearby magnet will be shown.