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Acoustic measurements of bouncing balls and the determination of gravitational acceleration
1.B. V. Pape, “Fallbeschleunigung mit einem hüpfenden Ball” (translated as “Determining acceleration of free fall with Super Ball”), Praxis der Naturwissenschaften — Physik in der Schule (translated as Practice of Sciences — Physics in School), 4/49, 28–32 (Aug. 2000).
2.G. Sprockhoff, Physikalische Schulversuche, Mechanik (translated as Physical Experiments in School, Mechanics) (Oldenbourg Verlag, Munich/Düsseldorf, 1961).
3.O. Schwarz and P. Vogt, “Akustische Messungen an springenden Bällen” (translated as “Acoustic measurements of bouncing balls”), Praxis der Naturwissenschaften — Physik in der Schule (translated as Practice of Sciences — Physics in School), 3/53, 22–25 (June 2004).
4.J. A. White, A. Medina, F. L. Román, and S. Velasco, “A measurement of g listening to falling balls,” Phys. Teach. 45, 175–177 (March 2007).
5.C. E. Aguiar and F. Laudares, “Listening to the coefficient of restitution and the gravitational acceleration of a bouncing ball,” Am. J. Phys. 71, 499–501 (May 2003).
7.Alternatively, a commercial measuring system or a free sound editor (e.g., Audacity) can be used to make the acoustic recordings.
8.The kinetic energies and between two subsequent impacts behave like the squares of the impact velocities, and the rise and fall times of the ball are given with . Thereby we measure the time between two impacts, i.e., .
9.J. Kuhn and P. Vogt, “Smartphones as experimental tools: Different methods to determine the gravitational acceleration in classroom physics by using everyday devices,” Eur. J. Phys. Educ. 4 (1), 16–27 (Jan. 2013).
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Interesting experiments can be performed and fundamental physical relationships can be explored with so-called Super Balls or bouncy balls. An example is the determination of gravity g in an experiment. The basic idea behind this was described by Pape1 and Sprockhoff2: The initial and final heights and the complete duration of all the bounces are measured for a certain number of bounces by the ball. On the basis of this data, the acceleration of gravity can be approximately calculated if air drag on the ball is neglected. However, in practice, it becomes clear that measuring the height of the last bounce in the process is problematic. The person performing the experiment either has to make a good estimation of its height or film the bounce in front of a measuring stick. The method is based on the important assumption that each of the individual bounces of the ball loses the same percentage of mechanical energy; the coefficient of restitution k therefore remains the same.
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