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We know that sound travels faster in a water than air. Also water is denser than air. So sound travels faster in a denser medium.

But we know that sound travels faster in a warmer air and warmer air lighter than less warm air.

Then how is it possible? First, sound travels faster is a denser medium. But then we see sound travels faster in a lighter medium. I don't see where I'm mistaken?

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All else being equal, sound travels slower in a denser medium. Sound travels faster in water than air, and faster in steel than water because these materials have a higher elastic modulus.

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  • $\begingroup$ What is this elastic module? $\endgroup$ – Theoretical Feb 12 '18 at 6:16
  • $\begingroup$ The stiffness of the material. $\endgroup$ – Ben51 Feb 12 '18 at 6:18
  • $\begingroup$ stiff material = faster transmission. soft material = slower transmission. $\endgroup$ – niels nielsen Feb 12 '18 at 6:27
  • $\begingroup$ @niels nielsen Can I get the mathematics? $\endgroup$ – Theoretical Feb 12 '18 at 7:20
  • $\begingroup$ here you go $\endgroup$ – Ben51 Feb 12 '18 at 7:22
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You say:

"But we know that sound travels faster in a warmer air and warmer air lighter than less warm air."

There is a problem with the logic used here. If the amount of air in an enclosure stays the same, and we heat it up, the air does not get lighter. What will happen is sound will travels faster in this warmer air since its molecules have more kinetic energy and collide more frequently, carrying the sound wave faster.

It is true that sound travels faster in denser air of the same temperature.

Your statement "...warmer air lighter than less warm air"

only 'seems' true because, for example in a hot air balloon, as the air gets heated, the pressure rises and some air gets pushed out of the balloon bottom, leaving less air in the hot air balloon, making it lighter. Similarly in the atmosphere, air heated by desert surfaces etc rises because it expands locally, decreasing in average density, while cooler air, which is denser, moves in below. This is all possible because the atmosphere is so vast and local variations are normal.

To clarify the thinking further, a body of air at $0^{\circ}$ Celsius, that is 90% vacuum is lighter than air at atmospheric pressure that is hotter by say $10^{\circ}$ Celsius.

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