Note that the scales differ between figures. Total displacement vectors in the first eigenmode.Īxial displacements only. The peak axial displacement is 0.03 and the displacement in the stem is 0.01. The mode is normalized so that the maximum total displacement is 1. The displacements are shown in the figures below. The stem has an essentially rigid axial motion, which is necessary for keeping the center of mass in a fixed position, as required by Newton’s second law.The bending of the prongs is accompanied with an up-down motion that varies linearly over the prong cross section.If we study the displacements in detail, it turns out that even though the overall motion of the prongs is in the transverse direction (the x direction in the picture), there are also some small vertical components (in the z direction), consisting of two parts: The mode shape for the fundamental frequency of the tuning fork. The tone of the device is a reference A4 (440 Hz), the material is stainless steel, and the total length is about 12 cm.įirst, let’s have a look at the displacement as the tuning fork is vibrating in its first eigenmode: The model is based on a tuning fork that one of my colleagues keeps in her handbag. To investigate this interesting behavior, we created a solid mechanics computational model of a tuning fork. The tabletop surface will act as a large loudspeaker diaphragm. The motion is much smaller than the transverse motion of the prongs, but it has the potential to set the large flat tabletop in motion - a surface that is a far better emitter of sound than the thin prongs of a tuning fork. When you hold the stem of the tuning fork to a table, an axial motion in the stem connects to the tabletop. You can hear it, but it is not a very efficient conversion of the mechanical vibration into acoustic pressure.
The pressure waves in the air propagate as sound. When you hold a vibrating tuning fork in your hand, the bending motion of the prongs sets the air around them in motion. As it turns out, the explanation behind this mystery can be boiled down to nonlinear solid mechanics. When you strike a tuning fork and hold it against a tabletop, it seems to double in frequency. In a recent video on YouTube from standupmaths, science enthusiasts Matt Parker and Hugh Hunt discuss and demonstrate the “mystery” of a tuning fork. In this blog post, we explain the tuning fork mystery using simulation and provide some fun facts about tuning forks along the way. The sounds waves travel to our ears.When a tuning fork is struck, and held against a tabletop, the peak frequency of the emitted sound doubles - a mysterious behavior that has left many people baffled. Describe the vibraion of the tuning fork causing the surrounding air molecules to vibrate.
Do the students notice a pattern?Students should notice that the higher the frequency (in Hertz) the higher the pitch of the tuning fork. Relate the speed of vibration of the tuning fork to the pitch Read the measurement of frequency in Hertz from each tuning fork to the group. What do the students notice? (The tuning forks have different pitches.) Part One - Pitch and frequencyĪfter students have had a few minutes to play with the tuning forks, listen separately to each student's tuning fork. Pass out tuning forks and have students hit them on their knee or the ball of their hands.
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