Hot chocolate effect

The hot chocolate effect is a phenomenon of wave mechanics in which the pitch heard from tapping a cup of hot liquid rises after the addition of a soluble powder.[1][2] It was first documented in 1980 by Frank Crawford of the Lawrence Berkeley Laboratory.[3] It was initially observed in the making of hot chocolate or instant coffee, but also occurs in other situations such as adding salt to supersaturated hot water or cold beer. Recent research has found many more substances which create the effect, even in initially non-supersaturated liquids.[4] The effect is thought to happen because upon initial stirring, entrained gas bubbles reduce the speed of sound in the liquid, lowering the frequency. As the bubbles clear, sound travels faster in the liquid and the frequency increases.

The effect can be observed by pouring hot milk or hot water into a mug, stirring in chocolate powder, and tapping the bottom of the mug with a spoon. The pitch of the taps will increase progressively with no relation to the speed or force of tapping. Subsequent stirring of the same solution (without adding more chocolate powder) will gradually decrease the pitch again, followed by another increase. This process can be repeated a number of times, until equilibrium has been reached.[5] Musical effects can be achieved by varying the strength and timing of the stirring action along with the timing of the tapping action.[6]

Origin of the phenomenon

The phenomenon is explained by the effect of bubble density on the speed of sound in the liquid. The note heard is the frequency of a standing wave where a quarter wavelength is the distance between the base of the mug and the liquid surface. This frequency f is equal to the speed v of the wave divided by four times the height of the water column h:

The speed of sound v in a homogeneous liquid or gas is dependent on the fluid's mass density () and adiabatic bulk modulus (), according to the Newton-Laplace formula:

Water is approximately 800 times denser than air, and air is approximately 15,000 times more compressible than water. (Compressibility is the inverse of the bulk modulus .) When water is filled with air bubbles, the fluid's density is still very close to the density of water, but the compressibility will be the compressibility of air. This greatly reduces the speed of sound in the liquid. Wavelength is constant for a given volume of fluid; therefore the frequency (pitch) of the sound will decrease as long as gas bubbles are present.[1]

Different rates of bubble formation will generate different acoustic profiles, allowing differentiation of the added solutes.[4][7][8]

See also

References
  1. Frank S. Crawford, May 1982, "The hot chocolate effect", American Journal of Physics, Volume 50, Issue 5, pp. 398-404, doi:10.1119/1.13080 (Abstract only)
  2. Frank S. Crawford, November 1990, "Hot water, fresh beer, and salt", American Journal of Physics, Volume 58, Issue 11, pp. 1033-1036, doi:10.1119/1.16268 (Abstract only)
  3. Frank S. Crawford, December 1980, "The hot chocolate effect", Lawrence Berkeley National Laboratory, Preprint
  4. D. Fitzpatrick et al., March 2012, "Principles and Applications of Broadband Acoustic Resonance Dissolution Spectroscopy (BARDS): A Sound Approach for the Analysis of Compounds", Analytical Chemistry, Volume 84, Issue 5, pp. 2202-2210, doi:10.1021/ac202509s
  5. The Hot Chocolate Effect. Archived from the original on 2021-12-15.
  6. The Hot Chocolate Effect (and making music with it) on YouTube
  7. D. Fitzpatrick et al., 2012, "Blend uniformity analysis of pharmaceutical products by Broadband Acoustic Resonance Dissolution Spectroscopy (BARDS)", International Journal of Pharmaceutics, Volume 438, Issue 1-2, pp. 134-139, doi:10.1016/j.ijpharm.2012.07.073
  8. D. Fitzpatrick et al., 2013, "The relationship between dissolution, gas oversaturation and outgassing of solutions determined by Broadband Acoustic Resonance Dissolution Spectroscopy (BARDS)", Analyst, Volume 138, Issue 17, pp. 5005-5010, doi:10.1039/C3AN36838F
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