Superposition of sound waves: beats

An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave packets. In general, the peak of a wave packet travels at a speed equal to the magnitude of the group velocity that can be vastly different than the phase speeds of the component harmonic waves, even if the entire set of harmonic waves only differ among themselves slightly in frequency and wavelength. It is difficult for students to understand the origin of this difference from verbal descriptions and static graphs of wave functions at successive instants in times, such as are typically presented in textbooks. However, considerable insight is possible using the free online software Desmos.

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Demonstrating Mechanical Beats on Phosphorescent Foil in Real Time

Lazos

Nezis²,

Kyriazopoulos³

2022

The Physics Teacher

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The interference pattern between two harmonic oscillations with slightly different frequencies are called beats. The beats, as a combined motion, have two different periods, one approximately equal to the period of the original oscillations, and another that is significantly longer and is related to the variable amplitude of the motion. The main objective of this presented work is to engage students’ attention and demonstrate in a simple way the concept of mechanical beats as a resultant motion of combined oscillations, but also to experience it through a visual projection. The proposed experimental setup is constructed in a way that satisfies both objectives and it consists of two parts that allow us to demonstrate in real time the combination of two harmonic motions. In the first part, the resultant motion is generated by the oscillations of two parallel rulers equipped with mirrors, and in the second part the visual demonstration of the beat occurs on a phosphorescent rotating foil by using a blue violet laser beam.

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Superposition of sound waves: beats

Cited by 3 publications

References 3 publications

Sound beats experiment using single and double smartphone with tone generator application and audacity

Sound beats experiment using single and double smartphone with tone generator application and audacity

Using Desmos to Understand the Difference Between Phase and Group Velocity

Demonstrating Mechanical Beats on Phosphorescent Foil in Real Time

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