Question about the whistling jelly balls

Question

In this video you can see little jelly balls that start jumping up and down when put in a heated pan. The explanation is that the balls release little puffs of steam, at a certain rate. But why does that sounds (well, a bit) like whistling? Is the sound caused by this released puffs of steam, or just because of the interaction of the balls with the heated pan (which seems more plausible to me)?

Answer 1

The sound is definitely being caused by the balls interacting with the pan.

This article does a fair job explaining the effect.

To find out what was happening, the team focused a high-speed camera on the interface between the ball and the pan. “We saw a gap under the ball that opened and closed 2000-3000 times per second, like the piston of an engine,” says Waitukatis.

Every time a ball hit the pan, in the fraction of a second it was in contact, steam built up under the elastic surface until the gel was forced to curve up and release the vapor. This is similar to the Leidenfrost effect, in which steam cushions form under water droplets on a hot pan, causing them to skate around like hovercrafts.

Once the steam was released from under the gel, the material’s elasticity forced the bottom to rebound back onto the hot plate, and the process repeated, about 10-15 times for each bounce. These “micro-slaps” occur because water in the gel vaporises on contact and presses back up on the ball, generating kinetic energy that sends the balls leaping to surprising heights over and over again.

The frequency of the slapping matched the frequency of the shriek, suggesting the ball is acting like a speaker, vibrating the air to make sound. The energy pumped into the ball eventually helped propel it back up into the air. Four centimetres was the height at which the energy provided by the hot plate during each bounce balanced the energy lost on impact, at least for a few minutes. At different temperatures and with different formulations for the gel, that sweet spot would be different.

---

What's really interesting about this video is that the smaller balls appear to have a higher pitched sound to them. Conveniently the maker of the video bounces several balls by themselves first. We can take a look at the frequency content by performing an FFT on the audio recording for each type.

This image shows the relative pressure energy across the frequency spectrum. Overall it's not the clearest harmonic series, but we can see some peaks.

Both the large and small bead resonate at about 1653, 1913, and 2028 ± 10 Hz. (Remember the article's gaps opening and closing "2000 - 3000 times per second". These are fairly close and might be due to a different gel formulation or pan temperature.) But we can see that the small bead has some contributions from much higher frequency energy: 5322 and 8773 Hz.

Thus it sounds a bit higher pitched.

---

I became curious to see if any part of these harmonic series could be explained by the acoustic theory of bouncing spheres. In this freely available paper by Dan Russell at PSU, the author describes the expected resonant frequencies of a dribbled basketball, which is helpful.

He gives us the following equation to predict the resonant frequency of the sphere, itself:

$$f_{n \ell} = \frac{z_{n \ell} \ c}{2 \pi a}$$

Where $c$ is the speed of sound inside the hydrogel ball (there's good evidence that hydrogels don't vary much from water, or ~1500 m/s), $a$ is the characteristic length of the sphere (the author uses it's radius), and $z_{n \ell}$ is the somewhat daunting "$n$th zero of the derivative of the spherical Bessel function of order $\ell$".

Thankfully the author calculates the roots for us (pg. 551), arriving at:

roots $k_{n0}a = 0, 4.49, 7.73, 10.90, 14.07...$

The medium (purple) bead has the same diameter as the person's thumb in the video - let's say $0.016 \ m$. The small (teal) bead is about half that, or $0.008 \ m$.

Plugging in values for the (2,0,0) radial mode of the larger bead, we get:

$$f_{n \ell} = \frac{4.49 \ 1500}{2 \pi \ 0.016}= 66994 \ Hz$$

So for the lowest frequency mode of the larger ball, the resonant frequencies are already higher than we can hear. We can be almost certain that the source of the sound doesn't come from the bead, itself, vibrating. It's mostly coming from the bead striking the pan.