I know we say that the speed of sound is most in solids because the particles are closely packed to each other,so,the energy transfer can take place easily compared to when they are farther in air or liquid,but,then we say that hot air makes sound travel faster,but why? doesn't the particles in hot air further away from each other?so the speed there should be even less,why does it increase?are not we contradicting our own statement,can someone explain?
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$\begingroup$ Hi, please provide references for each claim made so that we can better assess the question and the specific scenarios. $\endgroup$– Carl WitthoftCommented Mar 2, 2022 at 18:39
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In a wave information is transferred via interactions between particles and with a gas the interaction is collisions between the molecules.
What you are suggesting is that as the temperature rises the molecules move faster but at the same as the density of the gas has decreased there is a compensation factor due to the separation of the molecules increasing.
So the molecules are moving faster but have further to go.
The ideal gas equation is of the form $PV = mRT$.
Consider a mole of gas at constant pressure, $P$.
If the temperature, $T$, is increased the volume, $V$, of the gas must also increase.
However note that the temperature is related to the $\text{(speed of molecules)}^2$ and the volume to the $\text{(separation of molecules)}^3$, thus speed and separation are not proportional to one another.
Let's assume that the volume is doubled then the separation between molecules has been increase by a smaller factor, $\sqrt[3] 2$, than the speed $\sqrt 2$ which means that information is transmitted faster at a higher temperature.
This explanation is not rigorous but is intended to show that there is reason to believe that as the temperature of a gas is increased so does the speed of sound through it.
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1$\begingroup$ So basically,the fact that particles are made to go further away from each other is compensated by the fact that each particle has more natural kinetic energy sort of thing,and the latter factor plays a bigger role and thus,hot air has higher speed of sound right? $\endgroup$ Commented Mar 2, 2022 at 9:17
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$\begingroup$ Like Aakash asked - is this for air getting hotter while constrained in volume, or while NOT constrained? $\endgroup$ Commented Mar 2, 2022 at 18:38
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$\begingroup$ @CarlWitthoft I assumed that the pressure stays constant as the temperature rises so the volume increases. $\endgroup$– FarcherCommented Mar 2, 2022 at 19:16