Cappuccino effect

The cappuccino effect is the name given to the acoustic phenomenon that occurs immediately after stirring a cup of cappuccino : if you knock the cup several times with the spoon, the pitch increases audibly within the first few seconds. This effect can be repeated after stirring again as long as there is still milk foam. The phenomenon was scientifically described in 1982 by Frank Crawford , who refers to WE Farrell, DP McKenzie and RL Parker, among others. In English, the effect is known as the "hot chocolate effect".

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

Physical explanation

The air bubbles that appear in the liquid as a result of stirring or adding salt lead to a drastically reduced speed of sound . A content of 1% air bubbles reduces the speed of sound in water from around 1500 m / s to 120 m / s, which is lower than in air (343 m / s at 20 ° C). That the speed drops so much is initially surprising. The surprise comes from the fact that one intuitively assumes that there should be some kind of mean value for the speed of sound between air and water, as Crawford aptly points out. In fact, the speed of sound depends on the density and compressibility of a medium. A high density causes a low speed of sound, and a high compressibility also causes a low speed of sound. Compared to air, water has a high density, but a comparatively negligible compressibility. The two effects on the speed of sound are opposite and can only be determined by an exact calculation (see Crawford). In the case of water, the result is a comparatively high speed of sound; the effect, brought about by the low compressibility, thus predominates. If air is added to the water in the form of bubbles, the density hardly changes, but the compressibility does. This increases strongly, so strongly that it can lead to a lower speed of sound compared to air.

In general, the higher the frequency of the tone , the higher the pitch that is perceived, the higher it appears . The frequency, in turn, is related to the speed of sound and the wavelength of the sound wave: ${\ displaystyle f}$ ${\ displaystyle v}$ ${\ displaystyle \ lambda}$

{\ displaystyle f = {\ frac {v} {\ lambda}}}

If the speed of sound (or ) changes as in the phenomenon observed here, the pitch does not necessarily have to change too. The formula also allows the wavelength to change to the same extent and the pitch to remain unchanged. This is the case, for example, when you utter a scream underwater. In this case, the pitch is not changed, but the wavelength. In the present case, however, there is a special feature: a standing wave forms between the bottom of the vessel and the surface of the liquid when knocking . Such a standing wave has a length that depends on the dimensions of the vessel. is therefore fixed and cannot change. It follows that the pitch must change when the speed of sound is changed. ${\ displaystyle v}$ ${\ displaystyle c}$ ${\ displaystyle f}$ ${\ displaystyle \ lambda}$ ${\ displaystyle v}$ ${\ displaystyle f}$ ${\ displaystyle \ lambda}$ ${\ displaystyle f}$ ${\ displaystyle v}$

This means that the frequency increases as the speed of propagation increases. Since the number of bubbles dissolved in the liquid decreases continuously as it rises to the surface, the compressibility of the liquid also decreases. As a result, the speed of propagation and thus the frequency of the standing wave increase, which leads to the audible increase in pitch.

Remarks

↑ Strictly speaking, this only applies if you use a vessel that is very high compared to its diameter, and you have to knock against the floor from below. If you use a normal cup and tap the edge on the side, many other waves are also created. The phenomenon can still be observed, but it is no longer that easy to explain.

Web links

Hot knowledge The cappuccino effect . ( Memento from June 4, 2013 in the Internet Archive ) DRadio Knowledge
Video on Youtube

Individual evidence

↑ ^a ^b ^c Frank Crawford: The hot chocolate effect . In: American Journal of Physics . tape 50 , no. 5 , May 1982, pp. 398-404 , doi : 10.1119 / 1.13080 .
^ WE Farrell, DP McKenzie, RL Parker: On the note emitted from a mug while mixing instant coffee . In Proc. Cambridge Philosophical Society , Vol. 65, 1969, p. 365.
^ Frank Crawford: Hot water, fresh beer, and salt . In: American Journal of Physics . 58, No. 11, November 1990, pp. 1033-1036.
↑ The Sounds of teacups and Glasses . DrPhysics. Retrieved January 20, 2010.

[5] Strictly speaking, this only applies if you use a vessel that is very high compared to its diameter, and you have to knock against the floor from below. If you use a normal cup and tap the edge on the side, many other waves are also created. The phenomenon can still be observed, but it is no longer that easy to explain.

[craw1-1] Frank Crawford: The hot chocolate effect . In: American Journal of Physics . tape 50 , no. 5 , May 1982, pp. 398-404 , doi : 10.1119 / 1.13080 .

[fare1-2] WE Farrell, DP McKenzie, RL Parker: On the note emitted from a mug while mixing instant coffee . In Proc. Cambridge Philosophical Society , Vol. 65, 1969, p. 365.

[craw2-3] Frank Crawford: Hot water, fresh beer, and salt . In: American Journal of Physics . 58, No. 11, November 1990, pp. 1033-1036.

[4] The Sounds of teacups and Glasses . DrPhysics. Retrieved January 20, 2010.