# Can we measure temperature of a object just by the sound it makes?

I been thinking if temperature is a basic property of macroscopic objects rather than of quantum or microscopic objects and it is as a result of average kinetic energy of particles residing in the object either through movement of vibration.

That being said, its also described similarly in Wikipedia thus I'm sure it is a good description of temperature however this is the only description I'll use for this question but there are way more descriptions of temperature.

That however is similar to sound which is also as a result of vibration in an medium which will result in transfer due to vibrations and movement of particles being oscillated through the medium which will transfer the energy across.

That being said cant we detect a temperature just by hearing it using a detector but obviously we have to know its vital information like density of the medium and density of the material and such but not the temperature of the object

Can this be possible?

I'm in middle school so please excuse my lack of scientific knowledge therefore if any descriptions are mathematical please explain it.

• How would the object make a sound? Are you asking about the sound of dropping it - like from this awesome SE post? Jul 10 '14 at 18:24
• Do you mean that you do something like strike an object and measure the resulting frequency? Kind of like taking a tuning fork and heating it up then striking it and finding it's temperature knowing the new and original frequencies? Jul 10 '14 at 22:04
• I mean that leaving the object inside a sound frequency detector which will measure any sort of particles bouncing as a result of heat and this particles will behave like sound and be heard by the detector Jul 10 '14 at 22:06
• A related note: if your shower spray hits your shower curtain, then you can hear the impact sound change as the water warms up. Sep 12 '15 at 0:57

## 2 Answers

Have a look at this black body radiation spectrum, which is approximately the spectrum of "light", electromagnetic radiation, that a body radiates because of the intrinsic kinetic degrees of freedom of the molecules.

Look at the frequency spectrum for 300K, about room temperature. Acoustic frequencies are of the order of a few thousand Hertz, infrared is orders of magnitude more variable per second than sound.

Sound is vibrations by collective lattices/volumes composed of order of 10^23 molecules, which when vibrating mechanically, altogether, displace the air molecules and transfer the vibrations to the air that we hear as sound.

So it is possible to measure temperature of matter by the electromagnetic radiation it radiates at that temperature, but sound has no one-to-one connection with this radiation.

This page gives a chart of Young's modulus over temperature for various metals. Taking the top line of the table, the modulus drops from 31.4 Msi at -325F (-200C) to 24.2 Msi at 800F (427C). Due to thermal expansion, you will have more square inches. Using a linear expansion of $12E-6 K^{-1}$ the area of a bar will increase $1.5\%$ The longitudinal frequency will then drop from $1$ to $\sqrt{\frac {24.2}{31.4}\cdot 1.015} \approx 0.88$ over that range. It isn't very sensitive, but you can get some indication.

• Wouldn't that mean that you can only detect temperature-caused sound from a metal while it has not reached thermal equilibrium? Jul 10 '14 at 22:22
• No, I was looking at changes in the normal modes. If you know what the bar frequency is at one temperature, this tells you how it changes. So hit the end, measure the frequency of vibration, and compute the temperature based on the frequency shift from your initial measurement. Jul 10 '14 at 23:20