![]() ![]() This capability is available in the Acoustics Module and is illustrated below.Ī vibrating tuning fork with its surrounding air pressure wave as computed by the Acoustics Module. In COMSOL Multiphysics, you cannot only simulate the vibration of the tuning fork, but also its coupling to the surrounding air domain and the resulting acoustic pressure wave. However, in both cases, the fundamental balanced mode is at 440 Hz.Īs a side note (pun intended), the transient timbre of a tuning fork, including tonal contributions from the higher resonant modes, is what creates the characteristic sound of a Rhodes electric piano, which is essentially a collection of tuning forks, or tines, of different lengths. You get a slightly different set of modes in the case of a tuning fork that is unconstrained, such as if you hang it from a string. ![]() The pictures above correspond to a tuning fork that is constrained at the handle by someone holding it firmly. Created from a recording of a tuning fork using the software Cubase® 7.5 from Steinberg® Media Technologies GmbH. Peaks are clearly visible at 440 Hz and 2800 Hz, corresponding to modes that are balanced with little force transfer to the handle and, so, less damping. The first balanced higher mode that, again, transfers very little force to the handle is at 2800 Hz and will sound together with the fundamental mode when striking the tuning fork.Ī spectral analysis of a sounding tuning fork in real life indeed reveals this to be the case:Ī frequency spectrum of a ringing tuning fork dB vs. Many of the higher resonant modes have a twisting and rotational motion that transfer plenty of force to the handle and will be dampened out quickly by a hand holding it. This mode is weakly dampened and sustained the longest after a strike. The fundamental mode has the prongs vibrate back and forth in a symmetric and balanced fashion, which transfers very little force to the handle. The fundamental vibrational mode of a tuning fork at 440 Hz. The deformations are exaggerated to show the shapes more clearly. The pictures below show the qualitative mode shapes of a few of the first eigenmodes. Just a second or so after striking the fork, most of the higher modes are dampened out and all that can be heard is the sound of the fundamental mode as a clean tone. The higher eigenfrequencies correspond to resonant modes that will be dampened out more quickly than the lowest eigenfrequency of the so-called fundamental mode. Each mode is associated with a particular eigenfrequency and the combination of all eigenfrequencies creates the specific timbre that makes the characteristic sound of a tuning fork. When you strike a tuning fork, it will vibrate in a complex motion pattern that mathematically can be described as the superposition of so-called resonant modes, or eigenmodes. The mechanism of vibration is similar in all these cases, so let’s discuss that first. In addition to musical applications, there are industrial applications of tuning fork-like structures, such as in MEMS gyroscopes. The picture shows a tuning fork for the standard concert pitch 440 Hz. ![]() You can buy tuning forks corresponding to all of these standards, but also tuning forks for other notes such as C, E, and G. For example, the New York Philharmonic and the Boston Symphony Orchestra use 442 Hz and many orchestras in Europe use 443 Hz. However, there are also other standards in use, frequently based on the note A. The most common standard pitch is 440 Hz for the note A. This blog post will give you an overview of the Tuning Fork application and the structural vibration model that it is based on.Ī tuning fork is used to calibrate instruments to a standard pitch. In order to make it easy to get started with the Application Builder, we included a few example applications in the Application Libraries of COMSOL Multiphysics version 5.0. ![]()
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