So, the speed of sound is 340 m/s in air, but it’s much higher in water. I’ve gotten the explanation that the density of a medium determines the speed of sound in the medium. The more dense, the lower the speed of sound. I’m wondering if there are other factors that determine the speed of sound?
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1$\begingroup$ The more dense, the higher the speed of sound. The more dense, the lower the speed of sound. $\endgroup$– user4552Commented Feb 13, 2019 at 21:44
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$\begingroup$ @BenCrowell Yeah, you’re right, my mistake $\endgroup$– MelvinCommented Feb 13, 2019 at 21:48
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1$\begingroup$ Yes: the stiffness, given by Young's modulus $\endgroup$– FGSUZCommented Feb 13, 2019 at 22:04
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1$\begingroup$ As described here. $\endgroup$– ChemomechanicsCommented Feb 13, 2019 at 22:05
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1 Answer
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In general, $$v=\sqrt{\frac{B}{\varrho}},$$
where $B$ is the bulk modulus and $\varrho$ the density.
For ideal gases, the adiabatic bulk modulus is $\gamma p$, where $p$ is the pressure; for air $\gamma = 1.40$. So at atmospheric pressure this is about $10^5$ pascal.
The density of water is about $10^3$ times that of air. But the bulk modulus of water is much larger, $2.15$ GPa, so the speed of sound is about $\sqrt{20} \approx 5$ times higher in water than in air.