I'm asking this because I'm trying to find out what the speed of sound depends on.

I've figured out this far that it depends on the rigidity ("young's modulus") of the medium and the density.

However, now I just read that it also depends on the temperature, as vibrating molecules will have more energy to transfer onto each other.. this I do not understand.

So in case it does change.. is it because as you heat the metal it will also expand, causing the density to decrease, which should lead to a higher sound propagation?

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As you heat metal it becomes much weaker to resisting volumetric change and shear stresses (the bulk modulus (K) and shear modulus (mu) both reduce). Density (rho) reduces very slightly. You will be reducing the speed of sound (P wave velocity, Vp) substantially.

Vp = SqRt((K×4/3mu)/rho)

Casual physics reader here.

If we’re assuming the baseline to be room temperature, would that mean that colder temperatures increase the rate at which sound travels?

It's not straightforward, but in general yes

This opens up a whole slew of new questions for me.

-would each metal would have different thresholds for the rates at which speed could travel through it? (Assuming no sound is held at boiling point due to a change in state)

-would it have different rates of travel as a liquid than a solid, or would we expect a similar waveform?

-is Freezing point the upward maximum for cold? (Because there’s still technically space between atoms at freezing point) if not, how would the rate of travel be predicted to react to drops in temperature past the freezing point (until there’s minimum/no space between atoms)?

Sound can travel through any medium except vacuum. Temperature is only enforcing a control because it changes other physical and mechanical properties of a material. Its better to think about those different parameters individually, because the temperature effects are non linear, and vary by material.

Remember- freezing point is simply the point at which a liquid becomes solid (typically we talk about this for water, which occurs at 0 centigrade at standard pressure). We can still transfer pressure waves, the state of matter will change the speed though.

Do you know if there’s any research/reading material available that shows the differences by metal?

Sorry, don’t wanna bog you down with questions lol.

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I only really deal with it in rocks. The same physics applies to all metals (and other materials!). There's a huge amount of metallurgy research though - look for stuff on young's modulus, bulk modulus and shear modulus. P wave velocities (sound wave, acoustic wave, compression wave - all mean the same thing) aren't used as much in metal analysis, but they are used. You can use the moduli and density data to work out how P wave will respond though.

Sweet! Thanks for pointing me the right way.

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> when a metal is heated, its density decreases while its stiffness increases

Metals generally don't get stiffer with increasing temperature.

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Doesn’t the stiffness decrease? Isn’t that how blacksmiths were able to form swords, by heating them up?

Just a warning that the answer for "temperature effect on sound speed" will be totally different for air vs solids.

In air, sound speed depends strictly on temperature. This is because the bulk modulus of air is proportional to the pressure, so the sound speed is proportional to sqrt(pressure/density). By the ideal gas law, that means that sound speed is proportional to sqrt(temperature).

In solids, the effects of temperature on density and elastic moduli are not so simple as in gases. Also, in solids, there are both compressional and shear waves, vs just compressional waves in liquids/gases. Unfortunately, it's sometimes not clear from scientific writing on elastic waves in solids whether they're talking about compressional or shear waves (or both). In most cases I know of, higher temperature means lower elastic wave speeds because the effect on elastic modulus is stronger, especially for shear waves.

thank you!