Hot chocolate effect

Cappuccino effect is called the acoustic phenomenon that occurs immediately after stirring a cup of cappuccino: you knock the spoon several times in succession to the cup, as the pitch increases within the first few seconds of clearly audible. This effect can be, after renewed agitation, repeat as long as there is still milk foam. The phenomenon was scientifically described in 1982 by Frank Crawford, who refers among other things to WE Farrell, DP McKenzie and RL Parker. In English, the effect is called Hot Chocolate Effect.

The phenomenon can also be observed when salt is added to a glass of hot water or cold beer.

Physical explanation

The air bubbles occur in the liquid by stirring, or the addition of salt result in a drastically reduced sound speed. A content of from 1 % of air bubbles reduces the speed of sound in water of 1500 m / s to 120 m / s, which is lower than in air ( 343 m / s at 20 ° C). The fact that the speed decreases so is initially surprising. The surprise comes from the fact that one intuitively assumes that a kind of average of the sound velocities should arise between air and water, as Crawford aptly. But in fact it is so that the speed of sound depends on the density and compressibility of a medium. A high density results in a low speed of sound, and also causes a high compressibility of a low speed of sound. Water has a high density compared to air, but a comparatively vanishing compressibility. The two effects on the speed of sound in opposite directions and can only be determined by an exact calculation (see Crawford ). The result is water with a relatively high speed of sound, the effect caused by the low compressibility, so predominates. Now, if air is given in the form of bubbles in the water, the density hardly changes, but rather the compressibility. This increases greatly, so strong that it can come to a lower sound compared to the air velocity in the consequence.

In general, for the pitch, one perceives that they appear to be higher the more, the higher the frequency of the tone. The frequency, in turn, is related to the speed of sound and the wavelength of the acoustic wave:

Now if the speed of sound (or) as in the phenomenon observed here changes the pitch needs to change not necessarily. The formula also makes it possible that the wavelength to the same extent as the pitch changed and it remains unchanged. This is for example the case when one lets out a cry under water. The pitch will not be changed in this case, but the wavelength. In the present case one has but present a special feature: the tundish bottom and liquid surface a standing wave [Notes 1] is formed from at knock Such a standing wave has a length that depends on the dimensions of the vessel.. So is fixed and can not change. It follows that the pitch has to change, if the velocity of sound is changed.

This means that here the frequency increases with increasing propagation speed. As the number of dissolved in the liquid bubbles decreases continuously rise to the surface, also reduces the compressibility of the liquid. As a result, to increase the propagation velocity and thus the frequency of the standing wave, resulting in the increase in the pitch of the audible.