“A basketball bounced on a stiff surface produces a characteristic loud thump, followed by high pitched ringing,” says Joanthan Katz at Washington University in St Louis.
The question is why and, conveniently, Katz provides the answer on the arXiv today.
He assumes first that a basketball is an inextensible but perfectly flexible hollow sphere.
From this, he calculates that the thump is the result of the change of shape of the ball as it deforms when hitting a hard surface.
This creates a monopole source of sound that goes through only one full cycle of its frequency (of about 82 Hz for a full-sized basketball), hence the dull thump.
The ringing is caused by what Katz calls a dipole emission of sound and is essentially the vibration of the air within the basketball after the impact.
That’s a neat bit of calculating and Katz is honest to fault when it comes to pointing out the weaknesses of his model. He says, for example, that while the assumption of intextensibility is reasonable, perfect flexibility is a vast simplification that is necessary to make the problem tractable.
However, he says assuming the opposite–that the ball has an extensible membrane and an incompressible filling fluid–produces neither a thump nor a ring.
If you’ve ever dropped a balloon filled with water, you’ll know what he means.
Ref: arxiv.org/abs/0808.3278: Thump, Ring: the Sound of a Bouncing Ball