Can sound travel through dark matter

Why does the spoon sound change while I stir coffee?

An experiment for the coffee gossip: The sound that a spoon makes on a cup changes when one cappuccino is stirred well. If you repeatedly knock on the cup after stirring with the spoon, the noise changes over several seconds from a dull "clang" to a bright "clink". This "cappuccino effect" also works with beer or soda.

The coffee cup knocking came to scientific honor almost a quarter of a century ago: The physicist Frank Crawford from the University of Berkeley published his findings in the "American Journal of Physics" and thus laid the foundation that other researchers expanded and varied over time. In a nutshell, simplified and summarized: bubbles in the liquid make the difference. The denser the liquid, the higher the pitch.

Basic principle of the clay in the cup

The knocking makes the cup vibrate in the lower area, which is transferred to the adjacent medium. This is the air for the empty cup, the liquid for the full one. Which tone is played depends primarily on the height or filling level of the cup: when you hit the base, a standing longitudinal wave forms in the oscillating column of air - from the base to the edge of the cup. It delivers the lowest note from the empty cup, the basic note, which is then transmitted through the air to the ear. Overtones overlay the whole thing, but are less important here.

The sound of stirring coffee

When the cup is filled, for the sake of simplicity up to the rim, the standing wave forms in the column of liquid above the bottom. Although this has the same length as the previous column of air, sound waves run out around four times faster in liquid than in air. Sound spreads over the molecules of the medium - each vibrating molecule hits its neighbors and so passes on the movement.

Correspondingly, the speed of sound is higher, the more densely the molecules are packed: higher in solids than in liquids than in gases. In water at room temperature, a sound wave reaches around 1480 meters per second, in air only around 340 meters per second. With hot air or hot coffee, this only increases by a few meters.

And the following applies: the higher the speed of sound in the medium, the higher the frequency of the sound wave, i.e. the pitch. The physical formula is:

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

The frequency \ (f \) of the sound results from the propagation speed \ (v \) of the wave, divided by the wavelength \ (\ lambda \).

Conclusion 1: The keynote from the empty cup is deeper than that from the full one.

Air in the system

And now the cappuccino comes into play. If a cup of cappuccino or latte has been standing motionless on the table for a while, the bubbles are floating above all in it; in terms of the speed of sound - and pitch - it is roughly the full cup from the moment.

However, stirring changes the situation: the air bubbles in the milk foam are distributed throughout the entire volume of the liquid. Suddenly the molecules are less densely packed, the sound waves repeatedly hit braking bubbles as they pass through the liquid, and the speed of propagation decreases. Correspondingly, the pitch also goes down, it roughly approximates the sound of an air-filled cup. The tone sounds deeper and duller than before you stirred.

But in the course of a short time the bubbles gradually rise to the surface and the liquid clears up again - the air content drops, the sound waves travel faster again, the pitch rises continuously. Until, usually after a few seconds, they have reached the tone that was heard before stirring.

Conclusion 2: The more bubbles mixed into the liquid, the deeper the tone.

Basic attempt

To keep his experiment simple, Crawford had filled a tall glass cylinder with water and then tapped it vertically from the inside on the bottom of the vessel. In this simplest case, only a longitudinal wave is created, he writes: “If the cylinder is quickly filled with hot tap water full of dissolved air, the pitch of this mode can drop by almost three octaves during the first few seconds as the air comes out of the solution and forms vesicles. Then the pitch slowly increases as the bubbles rise to the surface ”. Crawford set up a simple equation for the ratio of the pitches and found a good match in experiment.

The experiment also works with other liquids. And the effect is also evident if the cup is only half full or if you hit the edge of the cup from the outside. This makes the calculation more complicated, however, because with half-full vessels, not only the fundamental tone of the liquid column but also the fundamental tone of the air column above must be taken into account. In addition to the longitudinal wave, the side stop also generates superimposed radial and circumferential vibrations in the cup and liquid.

In addition, the human ear is not always reliable when it comes to perceiving pitch. In this way, the brain can interpret a change in pitch in unclear sounds where there is none. And psychoacoustics is concerned with the fact that high frequencies are processed differently in the ear than low ones. For the cappuccino experiment, however, this is of little importance. The basic tone and its change are most evident in the case of nicely frothy drinks in good-sounding, not too shallow vessels.

variants

The basic principle of generating gas bubbles over the entire volume of a liquid as far as possible can be achieved in various ways. With cappuccino or hot chocolate, the protein molecules in the milk help envelop air bubbles and ensure a thick, fine foam. In a glass of beer, for example, bubbles are formed by stirring or sprinkling with sugar or salt: the spoon stirs in small amounts of air and, as it moves, makes the carbon dioxide dissolved in the beer pearl out - sugar or salt dissolve and thus ensure that that less carbon dioxide can be dissolved. It rises to the surface in bubbles.

With hot or cold water, air also reaches the lower regions if you sprinkle crumbs of soluble coffee or iced tea powder - the trapped air rises slowly to the surface. And very actively, effervescent powder or effervescent tablets bring gas bubbles into the water volume. The effect can be particularly noticeable if the hot water has previously been heated in the microwave and not stirred too vigorously: the hotter the water, the less air can be dissolved in it. But while the air coming out of the solution rises to the surface with audible bubbles forming in the kettle, the water in the microwave can be heated to just below the boiling point without the air rising: the water is now a supersaturated solution. Only when you stir or add salt or coffee powder does the air escape and form bubbles on crumbs or a spoon that rise to the top.