The Frequency of E320 Tuning Fork: Unraveling the Mystery of Sound Generation

The fascinating world of solid mechanics has long been shrouded in mystery, and one of the most intriguing phenomena is the frequency doubling of sound emitted by a tuning fork when struck against a tabletop. In this article, we will delve into the underlying principles that govern the behavior of the E320 tuning fork, providing an in-depth analysis of its mode shape and the factors contributing to the phenomenon.

To begin with, let's consider the physical properties of the E320 tuning fork. With a length of approximately 12 cm and made from stainless steel, this device produces a tone of reference A4 (440 Hz) when struck. The fundamental frequency of the tuning fork is characterized by its mode shape, which is crucial in understanding the behavior of the prongs as they vibrate.

According to studies, the peak axial displacement of the tuning fork is 0.03, while the displacement in the stem is approximately 0.01. Normalized so that the maximum total displacement is 1, these values provide a baseline for analyzing the motion of the prongs. The bending of the prongs is accompanied by an up-down motion varying linearly over the prong cross-section.

One of the key aspects of the E320 tuning fork's behavior is its axial motion in the stem when held against a tabletop. This motion is essential for maintaining the center of mass in a fixed position, as dictated by Newton's second law. Furthermore, the transverse direction of motion (in the x-direction) exhibits small vertical components (in the z-direction), consisting of two parts.

To investigate this phenomenon, we created a solid mechanics computational model of a tuning fork, inspired by the one kept in my colleague's handbag. Our model revealed that even though the overall motion of the prongs is transverse, there are indeed small vertical components present. These components, comprising both linear and nonlinear terms, contribute to the frequency doubling observed when the tuning fork is struck against a tabletop.

When you hold the stem of the tuning fork against a table, an axial motion connects the stem to the tabletop, allowing for efficient conversion of mechanical vibration into acoustic pressure. The pressure waves in the air then propagate as sound, resulting in the familiar tone emitted by the device.

The mystery surrounding the E320 tuning fork's behavior can be attributed to nonlinear solid mechanics principles. When struck and held against a table, the tuning fork seemingly doubles its frequency, which is not an efficient conversion of mechanical vibration into acoustic pressure. This phenomenon has left many people intrigued, and in this article, we have sought to provide an explanation through simulation.

In conclusion, the E320 tuning fork's behavior can be attributed to the complex interplay between its physical properties and nonlinear solid mechanics principles. By understanding the mode shape and axial motion of the prongs, we can unravel the mystery behind the frequency doubling phenomenon observed when striking a tuning fork against a tabletop.

Frequency of e320 tuning fork