Colfax Elementary - Ruler Sound Experiment

Phenomenon demonstration

https://youtu.be/ns5nHKBJiGg?si=TCQmdbUrY1i9shnI

How sound is produced? Experiment: swinging ruler - explained simply and clearly

Basic explanation of phenomenon

https://youtu.be/PYEsHvezfRY?si=vKZcyNRQl_xd10cB

Evaluation of sensor technologies for the rulers, a kalimba-like digital musical instrument

In this article, they present a discussion about the Rulers, a Digital Musical Instrument based on seven cantilever beams fixed at one end which can be bent, vibrated, or plucked. The instrument has already two sensing versions: one based on IR sensor, another on Hall sensor. They introduce strain gages as a third option for the Rulers, sensor that are widely used in industry for measuring loads and vibration.

https://www.researchgate.net/publication/266608335_Evaluation_of_sensor_technologies_for_the_rulers_a_kalimba-like_digital_musical_instrument

Flexural Vibration Test of a Beam Elastically Restrained at One End: A New Approach for Young’s Modulus Determination

A new vibration beam technique for the fast determination of the dynamic Young modulus is developed. The method is based on measuring the resonant frequency of flexural vibrations of a partially restrained rectangular beam. The strip-shaped specimen fixed at one end to a force sensor and free at the other forms the Euler Bernoulli cantilever beam with linear and torsion spring on the fixed end.

https://onlinelibrary.wiley.com/doi/10.1155/2013/329530

Twang! A physically derived synthesis model for the sound of a vibrating bar

A physically derived synthesis model of the sound generated when a ruler is twanged while hanging over the edge of a solid surface is presented. The model is derived from the Euler-Bernoulli equation, offering the user a set of physical parameters to control ruler length as well as the material properties.

https://eecs.qmul.ac.uk/%7Ejosh/documents/2022/Selfridge%20AES152.pdf

Physics-based sound synthesis of the vibrations of a cantilever steel beam using the finite element method

In the present work, a 2-dimensional computational model of a simple musical instrument: a cantilever beam surrounded by air, was built, and using finite elements, the sound produced by the beam when giving it an initial excitation was calculated. The synthesized sound was compared to a microphone recording of the sound produced by a real cantilever beam to verify that the synthesized soundwave had been calculated correctly. (PhD thesis)

https://www.academia.edu/92636301/Physics_based_sound_synthesis_of_the_vibrations_of_a_cantilever_steel_beam_using_the_finite_element_method

Sound with a ruler

Simple instructions for the experiment with further linked information and videos

https://www.ingridscience.ca/node/497

Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses

Online article which examining the vibrations of a straight, horizontal cantilever beam under a vertical load, which is susequently removed.

https://emweb.unl.edu/mechanics-pages/scott-whitney/325hweb/beams.htm