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The Speed VV Of Sound Waves in a Gas Like Air Might Plausibly

Question 7

Multiple Choice

The speed VV of sound waves in a gas like air might plausibly depend on the gas's pressure PP (which has units of N/m2\mathrm{N} / \mathrm{m}^{2} ) , the gas's density ρ\rho (which has units of kg/m3\mathrm{kg} / \mathrm{m}^{3} ) and its temperature TT (which has units of K\mathrm{K} ) , and some unitless constant CC . Assuming that no other quantities are relevant, which of the following formulas might possibly correctly give the speed of sound in a gas?


A) v=CPρTv=\mathrm{CP} \rho \mathrm{T}
B) v=CTP/ρv=\mathrm{CTP} / \rho
C) V=CP/ρV=\mathrm{CP} / \rho
D) v=CP/ρv=C \sqrt{P / \rho}
E) V=Cρ/PV=C \sqrt{\rho / P}
F) v=C(P/ρ) 2 v=\mathrm{C}(\mathrm{P} / \rho) ^{2}
G) None of these can be correct.

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