The resonance phenomenon is widely known in physics courses. Qualitatively speaking, resonance takes place in a driven oscillating system whenever the frequency approaches the natural frequency, resulting in maximal oscillatory amplitude. Very closely related to resonance is the phenomenon of mechanical beating, which occurs when the driving and natural frequencies of the system are slightly different. The frequency of the beat is just the difference of the natural and driving frequencies. Beats are very familiar in acoustic systems. There are several works in this journal on visualizing the beats in acoustic systems. For instance, the microphone and the speaker of two mobile devices were used in previous work to analyze the acoustic beats produced by two signals of close frequencies. The formation of beats can also be visualized in mechanical systems, such as a mass-spring system or a double-driven string. Here, the mechanical beats in a smartphone-spring system are directly visualized in a simple way. The frequency of the beats is measured by means of the acceleration sensor of a smartphone, which hangs from a spring attached to a mechanical driver. This laboratory experiment is suitable for both high school and first-year university physics courses.
Direct Visualization of Mechanical Beats by Means of an Oscillating Smartphone
Marcos H. Giménez, Isabel Salinas, Juan A. Monsoriu, Juan C. Castro-Palacio; Direct Visualization of Mechanical Beats by Means of an Oscillating Smartphone. Phys. Teach. 1 October 2017; 55 (7): 424–425. https://doi.org/10.1119/1.5003745
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