Which of the following graphs is correct?

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(C) $1$. For the velocity of sound in air, $v = \sqrt{\frac{\gamma P}{\rho}}$. Since $\rho = \frac{PM}{RT}$, we have $v = \sqrt{\frac{\gamma RT}{M}}$.

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(C) $1$. For the velocity of sound in air, $v = \sqrt{\frac{\gamma P}{ho}}$. Since $ho = \frac{PM}{RT}$, we have $v = \sqrt{\frac{\gamma RT}{M}}$. At constant temperature $(T)$, $v$ is independent of pressure $(P)$. Thus, the graph in option $A$ is incorrect as it shows $v$ increasing with $P$.$2$. The velocity of sound in air is $v = \sqrt{\frac{\gamma R(T_c + 273)}{M}}$. Thus, $v^2 = \frac{\gamma R}{M}(T_c + 273)$. This is a linear equation of the form $y = mx + c$ where $y = v^2$ and $x = T_c$. The graph in option $B$ shows a line passing through the origin, which is incorrect because at $T_c = 0^\circ C$, $v^2 
eq 0$.$3$. The velocity of a transverse wave in a string is $v = \sqrt{\frac{T}{\mu}}$, where $T$ is tension and $\mu$ is linear mass density. This implies $v^2 = \frac{1}{\mu}T$, or $v = \frac{1}{\sqrt{\mu}}\sqrt{T}$. This represents a parabolic relationship between $v$ and $T$. The graph in option $C$ correctly shows this parabolic dependence.Therefore, none of the individual graphs are correct as presented in the options, but based on standard physics problems of this type, option $C$ is the only physically accurate relationship depicted.

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