According to the ITF rules a "valid" tennis ball should bounce to between 135 cm and 147 cm when dropped on a concrete floor from a height of 254 cm (53-57 in from 100 in). This means that the ball should reach between 53% and 57% of the drop height when bouncing. However, that is a little difficult to measure, unless you have a high speed camera and are prepared to spend some time analyzing the video. Probably not something worth doing for checking and old can of balls.
A simpler way is to use the sound and a basic laws of physics. If you drop the ball and measure the time "t" between the first impact on the floor and the second, you can calculate the height "h" the ball has reached through the equation (g is gravity):
If you want to be more precise you can include the air resistance, which is fairly small, but will reduce the height with about 3 %. So including that and g=9.81 you get:
Since you take the square of the time you have to measure it fairly exactly. The easiest way to do it, is to record the sound with a computer, and get the time between the two bumps in the sound curve. Agreed that this still is a little work, but nothing that should prevent a scientifically minded tennis nerd
I have implemented this and some further calculation to handle low bounces in the latest version of racquetTune.
, tennis apps for the iPhone.