The speed of sound in mercury at a certain te | vedclass

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Question

(A) The speed of sound $v$ in a fluid is given by the formula $v = \sqrt{\frac{K}{\rho}}$,where $K$ is the bulk modulus and $\rho$ is the density of t

Vedclass · Accepted Answer

$2.86 	imes 10^{10} \, N/m^2$

Vedclass · Answer

(A) The speed of sound $v$ in a fluid is given by the formula $v = \sqrt{\frac{K}{ho}}$,where $K$ is the bulk modulus and $ho$ is the density of the medium.Squaring both sides,we get $v^2 = \frac{K}{ho}$.Rearranging for $K$,we have $K = v^2 ho$.Given $v = 1450 \, m/s$ and $ho = 13.6 	imes 10^3 \, kg/m^3$.Substituting the values: $K = (1450)^2 	imes (13.6 	imes 10^3)$.$K = 2102500 	imes 13.6 	imes 10^3$.$K = 28594000 	imes 10^3 = 2.8594 	imes 10^{10} \, N/m^2$.Rounding to two decimal places,$K \approx 2.86 	imes 10^{10} \, N/m^2$.

The speed of sound in mercury at a certain temperature is $1450 \, m/s$. Given the density of mercury as $13.6 \times 10^3 \, kg/m^3$,the bulk modulus for mercury is:

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