density of mediumtemperature of medium

The sources treated the topic fairly simplified although. Is there more to this?

Does the number of moles of molecules, the size of molecules and other factors also matter or is the speed of sound purely determined by these two factors (to an extent that would allow a formula to be made)?

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The speed of sound is found (both mathematically and experimentally) to be: $$ v = \sqrt{\frac{P}{\mu}}$$ . Let"s understand this formula a little, it depends on pressure directly (although to $1/2$ power) means if we increase the pressure the speed will be increased because more pressure means that molecules are hitting the walls of container strongly and hence are more energetic. If we make an ideal assumption that molecules can have only the kinetic energy and no potential energy then it"s a simple thing to conclude that more pressure means molecules are travelling faster (therefore hitting the walls more often and strongly) and therefore communicates or transfers the disturbance (that"s what sound is) more quickly.

The denominator $\mu$ is the mass density ( you can write it as $\rho$ and simply interpret it as density), all it tells us that how bulky our particles are, if they are bulkier then it would be harder to move them and hence the transfer of disturbance will be slower because our disturbance will cause only a little acceleration in them. Therefore, our speed is inversely proportional to th square root of $\mu$.

Now, let"s see your thing

I read in multiple sources that the speed of sound depends on:

1.density of medium 2.temperature of medium .

The sources treated the topic fairly simplified although. Is there more to this?

See, the density means mass per unit volume, i.e. how bulky are particles in one unit volume of the medium. If they are bulkier, then they will move slowly.

There are laws for gases and which relate pressure directly to temperature like

Ideal Gas Law $PV = NkT$ .

Van der Waals Eqaution $(P + \frac{an^2}{V^2})(V-nb) = nRT$ .

For the solids, the equation changes a little, it becomes $$ v = \sqrt{\frac{T}{\mu}}$$ where $T$ is the tension under which the solid is kept. Increasing the tension increases the volume which in turn decreases the density and hence the sound travels faster. With the increase in temperature, the solid expands and hence the density goes down, therefore the wave speed goes up.

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This may help you.