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I had the following thought experiment recently: Suppose we have a vibrating plate for which we can tune the amplitude and frequency of vibration, and imagine we hold a finger against the plate. For sufficiently high frequencies (presumably where it becomes impossible to perceive the phase of the vibration by touch), it seems that the vibration would be indistinguishable from heat.

Questions:

  1. Would such a vibration in fact feel like heat?
  2. At what frequency does this start to be the case?

Bonus:

  1. Are there quantitative scaling relationships between the frequency and amplitude of the vibration and the perceived temperature?

This seems to me to be more appropriate to physics SE than biology SE, but feel free to migrate if that's not the case.

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  • $\begingroup$ I don't think these sensations are perceived by the same mechanism. Touching something hot raises the temperature of your finger, which could cause different kinds of vibrations inside you. Whereas touching a vibrating plate is perceived by the physical contact with the outside of your skin. I could be wrong though. $\endgroup$ – HiddenBabel Feb 20 at 22:26
  • $\begingroup$ I dont think so, they seem to be actually sensing temperature en.wikipedia.org/wiki/Thermoreceptor $\endgroup$ – Wolphram jonny Feb 20 at 23:21
  • $\begingroup$ Ultrasound is a high strong vibration, there is something called ultrasonic welding but I think its more mechanical than thermal. But the concepts can get blurry. $\endgroup$ – PhysicsDave Feb 21 at 0:12
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This question, from a(n inanimate) physics viewpoint, seems closely related to asking whether increasing the speed of an object necessarily increases its temperature (under the reasoning that high temperatures generally involve faster molecular motion). It does not.

Thermal energy is characterized by random motion. In contrast, the vibrational motion you're describing is collective; it's a low-entropy phenomenon because it can be described by specifying a single mode and frequency, unlike the immense amount of position and velocity data that would be needed to describe the molecular motion occurring within a hot object.

It is, however, true that in any material (including the vibrating plate and your skin), vibrations are damped through internal friction. Fundamentally, this is a manifestation of material inelasticity, which is generally small for small deformations but never entirely absent. The resulting damping ultimately entirely converts vibration into thermal energy, which doesn't imply that these mechanisms are equivalent but only that one is converted into the other.

Let's now take a biological perspective. You've written "...it seems that the vibration would be indistinguishable from heat" and "The coupling of the motion of the plate to your skin will result in full spectrum of frequencies, which I strongly suspect would trigger your sense of heat in the same way as a genuinely random stimulus." Actually, vibration can induce feelings of cold, warmth, and/or pain depending on the conditions. There are multiple reports of reported skin sensations experimentally obtained from ultrasonic vibration applied to the skin; shown below is a typical configuration using 350 kHz or 650 kHz input (the upper bound of input frequency and amplitude is set by the emergence of frictional heating, as described earlier):


Lee et al., "Creation of various skin sensations using pulsed focused ultrasound: evidence for functional neuromodulation," International Journal of Imaging Systems and Technology 24.2 (2014): 167-174.

Here are reported (subjective) results from that paper for the highest frequency measured, 650 kHz:

Although the temperature of the water and finger stayed constant as measured by objective thermometry, when the subjects were in a 20°C environment, the self-reported sensation was that of cold (C); at 40°C, warmth (W) (see blue and yellow shading, respectively; in addition, "T" denotes vibration and "N" pain). These temperatures roughly correspond to the range of operation for the corresponding thermoreceptor, indicating that if you vibrate any thermoreceptor at the appropriate settings, you'll sense its corresponding output. Of course, that again doesn't mean that such vibrations are somehow equivalent to warmth any more than they're equivalent to cold. The authors compared the temperature sensations to those experienced when contacting menthol, for example, which has a cooling sensation even at room temperature because of receptor activation.

L. R. Gavrilov, a pioneer in characterizing human responses to focused ultrasonic exposure, reported that "By changing the intensity ard durations of the stimuli and also the location of the focal region, all sensations that humans can perceive through their skin, i.e., tactile, temperature (warmth and cold), different pain sensations and so forth, were induced." (Gavrilov et al., "Application of focused ultrasound for the stimulation of neural structures," Ultrasound Med Biol 1996; 22(2):179-92.) Gavrilov emphasizes that these are subjective sensations obtained with minimal actual induced temperature changes, further noting that "[w]ith some stimulus parameters (for instance, with a frequency of 2.67 MHz and duration of 100 msec) threshold sensations are accompanied by a significant increase (up to 10-15°C) in tissue temperature in the focal region, and this can doubtlessly produce temperature sensations." (Gavrilov et al., "The effect of focused ultrasound on the skin and deep nerve structures of man and animal," Progress in Brain Research vol. 43. Elsevier, 1976. 279-292).

In summary, large-amplitude and high-frequency vibrations can produce a temperature increase in materials due to internal damping and can produce sensations of cold or warmth (or pain) depending on the conditions (Gavrilov's reviews are a good starting point for understanding these results). However, I wouldn't say that a high-frequency vibration is equivalent to thermal energy (and for clarity, I'd avoid the use of heat as a noun).

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  • $\begingroup$ The fact that the question is asking about human perception makes this answer unsatisfactory. Whether or not you can, in principal, describe the plates' motion with a small amount of information has no bearing on the response of your thermal sensors. The coupling of the motion of the plate to your skin will result in full spectrum of frequencies, which I strongly suspect would trigger your sense of heat in the same way as a genuinely random stimulus. $\endgroup$ – Yly Feb 21 at 6:41
  • $\begingroup$ +1 Thanks for the edit. This now is a very useful answer. $\endgroup$ – Yly Feb 21 at 23:40
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Would such a vibration in fact feel like heat?

First of all, what the body senses is not heat. Heat is energy transfer due solely to temperature difference. What the body “feels” is the temperature of the affected tissue. Let’s say it’s the temperature of the skin.

If one were to touch a vibrating surface, the vibration could cause the skin tissues (epidermis and dermis) to vibrate. That vibration can cause friction in the tissue cells as they move relative to each other. The friction, in turn, may raise the temperature of the cells that would then be sensed by the nerve endings located within the dermis.

At what frequency does this start to be the case? Are there quantitative scaling relationships between the frequency and amplitude of the vibration and the perceived temperature?

The two questions are related as they both ask how to quantize the relationship between (a) vibration amplitude and frequency (b) the friction produced by such vibration frequency and amplitude (c) the temperature produced by the friction. To answer those questions, if answers do exist, would be the subject of research. One avenue you may want to pursue is information on the relationship between ultrasound and body tissue temperature.

ADDENDUM

This addendum is in reference to comments received as to what exactly causes us to feel that something is either “hot” or “cold”, or “hotter” or “colder”. The terms refer to our brains interpretation of electrical signals sent to it from sensory receptors (such as temperature, texture, and touch) located in the dermal layer of our skin. The sensory receptors that respond to temperature are referred to as thermoreceptors. Thermoreceptors detect temperature changes, according to the following link from an article in Scientific American.

https://www.scientificamerican.com/article/cold-or-warm-can-we-really-tell/

It has been debated in comments on this subject as to whether the thermoreceptors in our skin detect temperature change or heat (energy transfer to or from the skin due to temperature differences). In a sense it is both since it is heat transfer that manifests itself, or causes, temperature changes in the skin.

It has been shown in landmark studies, (1)(2)(3) below to name a few, that the threshold of pain and injury (2nd and 3rd degree burns) depend on the relationship of the combination of temperature at the surface of the skin and the duration (time) of exposure to that temperature. This relationship is, in turn, due to the rate of heat transfer per unit area to the skin (absorbed energy rate) and the duration (time) of the transfer.

So although the thermoreceptors are triggered by temperature changes, the temperature changes are due to heat transfer.

It has also been asked “..why staying in a pool of hot water feels less hot over time?”

As explained in the above referenced article, after a time the thermal receptors become desensitized (tire out) so that you no longer notice the sensation as much.

(1) A.R. Moritz and F.C. Henriques, Jr. Studies of Thermal Injury:II. The relative importance of Time and Surface Temperature in the Causation of Cutaneous Burns. American Journal of Pathology 23, 695-720.

(2) Stoll, AM, Greene LC: Relationship between pain and tissue damage due to thermal radiation. J. Appl Physiology 14:373-382, 1959

(3) Stoll, Alice M. John R. Piergallini and Maria A. Chianta. Thermal conduction effects in human skin: I, II, III. Report Nos. NADC-79033-60, -79034-60,-79036-60 15 January 1979.

Hope this helps.

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    $\begingroup$ "What the body 'feels' is the temperature of the affected tissue." This is not the case at all. It's really much closer to feeling heat than anything else- humans are sensitive to heat transfer into and out of tissues. If they felt the temperature of tissue directly, when you got into a bath you would feel hotter and hotter over time as your epidermis warmed, instead of the actual perception of getting used to the temperature as your epidermis warms, lowering the temperature differential and thus heat transfer into your skin. $\endgroup$ – Chris Feb 23 at 18:35
  • $\begingroup$ Chris, heat transfer to the body manifests itself as an increase in temperature of the tissue. The nerve endings in the dermis respond to the temperature of the dermis. You need to differentiate between the temperature of the tissue vs the temperature of a solid, liquid, or gas that the tissue contacts. A metal surface at the same temperature as a plastic surface feels hotter because the metal transfers heat to the skin at a faster rate, and thus increases the temperature of the skin at a faster rate. But still, it is the temperature of the skin that the body senses. $\endgroup$ – Bob D Feb 23 at 18:48
  • $\begingroup$ Then explain why staying in a pool of hot water feels less hot over time? The temperature of your skin is most certainly rising monotonically, so by your description the sensation should be that the water you are in is hotter and hotter over time. $\endgroup$ – Chris Feb 23 at 18:54
  • $\begingroup$ @Chris When you first get in a pool of hot water there is relative motion between your skin and the water causing forced convective heat transfer from the water to the skin making the water feel particularly hot. Over time, assuming you now remain still in the water, the water feels less hot since convection is no longer forced and there is a temperature gradient across a film of water in contact with the skin. But as anyone has taken a hot bath knows, you can make it feel hotter by moving your body in the water, increasing the rate of convective heat transfer to the skin. $\endgroup$ – Bob D Feb 23 at 19:09
  • $\begingroup$ The convection makes heat transfer to your skin larger, yes. But the whole time you're in the bath, your skin is heating up even more. So if your nerves sense the temperature of your skin directly, the temperature you feel should increase monotonically. It feels hotter when you move around because of convection because your nerves are sensing heat transfer, not the temperature of your skin. $\endgroup$ – Chris Feb 23 at 19:23

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