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(C) The energy density $(E)$ of a sound wave is given by the formula: $E = 2{\pi ^2}\rho {n^2}{A^2}$.Here,$\rho$ is the density of the medium,$n$ is t

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(C) The energy density $(E)$ of a sound wave is given by the formula: $E = 2{\pi ^2}\rho {n^2}{A^2}$.Here,$\rho$ is the density of the medium,$n$ is the frequency,and $A$ is the amplitude.The maximum speed of the particles of the medium is given by: ${v_{\max }} = \omega A = 2\pi nA$.Squaring the expression for ${v_{\max }}$,we get: ${({v_{\max }})^2} = 4{\pi ^2}{n^2}{A^2}$.Comparing the two expressions,we can see that $E = \frac{1}{2}\rho {({v_{\max }})^2}$.This implies that $E \propto {({v_{\max }})^2}$.Since $E$ is proportional to the square of ${v_{\max }}$,the graph between $E$ and ${v_{\max }}$ will be a parabola opening upwards,which is represented by Graph $C$.

$A$ sound source emits sound waves in a uniform medium. If energy density is $E$ and maximum speed of the particles of the medium is ${v_{\max }}$,the plot between $E$ and ${v_{\max }}$ is best represented by

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