The behaviour of a tennis racket is usually studied by impacting a ball at various positions on the string bed and measuring the ratio of the rebound to incident speed. This ratio is called the ACOR (Apparent Coefficient of Restitution). For this measurement, the racket is normally freely suspended, for example by balancing it vertically with the end of the handle on the floor. Alternatively, the racket can be held by hand, at rest, or the handle can be clamped in a vice. Players always swing the racket towards a ball, but it is easy to calculate the ball speed in this case, based on the ACOR measurements, simply by changing the frame of reference. One might think that the ball will bounce much better if the handle is held in a vice, or held firmly by the hand, but this is not the case. It turns out that the ACOR does not depend at all on how the handle is supported. A simple experiment was performed to investigate this effect, using a superball bounced at various points along a straight aluminium beam. It was found that, at distances more than 15 cm from each end, the ACOR is completely independent of the length of the beam or the method of support at each end or the distance of the impact point from the end. A theoretical analysis for a flexible beam shows why. The impact of a ball deforms the beam locally in the region around the impact area. This sends a transverse wave propagating away from the impact point at a speed of about 60 m/s, depending on the stiffness of the beam. The ball remains in contact with the beam for only about 5 ms. Meanwhile, the transverse wave heads off towards each end of the beam, reflects off each end, and heads back towards the ball. If the ball rebounds before the reflected waves arrive, then it has no way of knowing how long the beam is or whether the ends are clamped or freely supported. As a result, the ACOR is unaffected by the length of the beam or the method of support.
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