Conversion of Potential Energy: Sound or Heat?

When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?

There’s also the kinetic energy of the rebounding coin to consider, but one way or another it all ends up as heat eventually.
In principle we can measure the amplitude and duration of the sound waves and use that to calculate the amount of energy they carry away.

In practice this is the sort of calculation that we try to avoid,

Nugatory said:

In practice this is the sort of calculation that we try to avoid,

Yeah, just wait until the sound becomes heat too.

Darmstadtium said:

When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?

As a rule of thumb, sound is pretty low energy. This is because high density materials (like coins and counter-tops) can carry a lot of energy with a little motion while low density materials (like air) need a lot of motion in order to carry much energy at all. This means when the coin or countertop vibrate from an impact and the resulting motion is imparted to the air, not much energy is transferred. We say that the materials "couple" poorly.

If you have an interface between materials with similar densities, vibration energy passes through the interface easily. If you have an interface between materials with very different densities the vibration energy tends to reflect insead. This is very much analogous to the way that light behaves going between materials with a different refractive indices.

Consider, for instance, a tuning fork. It takes significant time to transfer vibration energy from fork to air.

If it was mostly sound, then a coin would bounce much higher in a vacuum.

Darmstadtium said:

When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?

Change the glass surface to something much louder, a steel drum for instance. If the noise increases by more than 3dB, this means that, with the glass, the kinetic energy of the coin was more than twice the sound energy. So the heat must be greater.

kered rettop said:

Change the glass surface to something much louder, a steel drum for instance. If the noise increases by more than 3dB, this means that, with the glass, the kinetic energy of the coin was more than twice the sound energy. So the heat must be greater.

This doesn't make any sense. If the noise increases by more than 3dB (power (intensity) level (SIL)) or 6dB (sound pressure level, SPL) that means the energy in the air has doubled. It tells you nothing about the kinetic energy in the coin and also nothing about the relative quantities of kinetic energy in the coin and air.

Arjan82 said:

This doesn't make any sense. If the noise increases by more than 3dB (power (intensity) level (SIL)) or 6dB (sound pressure level, SPL) that means the energy in the air has doubled. It tells you nothing about the kinetic energy in the coin and also nothing about the relative quantities of kinetic energy in the coin and air.

If you can drop the same coin from the same distance and get twice the sound energy out, that means that less than half of the coin's energy could have gone into the softer sound.

Similarly, if you can drop the same coin from the same distance and get four times the sound energy out, that means that less than 25% of the coin's energy could have gone into the softer sound.

To drive home the point of @jbriggs444. Look here for a table with sound powers for every day sources. Note for example:

A hair dryer puts 10^-6 Watt of acoustic energy in its surroundings, an accelerating motorcycle 0.1 Watt, A sonic boom of a Jet fighter is about 1 Watt. Note that these numbers are incredibly small compared to their kinetic energy or power consumption.

jbriggs444 said:

If you can drop the same coin from the same distance and get twice the sound energy out, that means that less than half of the coin's energy could have gone into the softer sound.

Similarly, if you can drop the same coin from the same distance and get four times the sound energy out, that means that less than 25% of the coin's energy could have gone into the softer sound.

Ah, ok, true.

[edit]Forget that last remark, the amount of input energy is the same of course[/edit]

Arjan82 said:

Ah, ok, true. But that's a bit of a stretch to me since you then also assume that both with the glass and drums you impart exactly the same amount of kinetic energy to the drums / glass. That might require a totally different hit.

The scenario in the OP, as I understand it has the coin striking a surface and ultimately coming to rest. Totally inelastic collision except for any sound energy that is radiated.

jbriggs444 said:

If you can drop the same coin from the same distance and get twice the sound energy out, that means that less than half of the coin's energy could have gone into the softer sound.

Similarly, if you can drop the same coin from the same distance and get four times the sound energy out, that means that less than 25% of the coin's energy could have gone into the softer sound.

Thanks

Ultimately, all the potential energy of the coin is converted into internal energy of the air (most of it), table (a tiny fraction), and coin (a tiny fraction). All the sound energy is dissipated to internal energy.