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(B) The bulk modulus $\beta$ is defined as $\beta = -\frac{\Delta P}{\Delta V / V}$.Given $\Delta P = 100 \, kPa = 10^5 \, Pa$ and the fractional chan

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$1414$

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(B) The bulk modulus $\beta$ is defined as $\beta = -\frac{\Delta P}{\Delta V / V}$.Given $\Delta P = 100 \, kPa = 10^5 \, Pa$ and the fractional change in volume $\frac{\Delta V}{V} = 5 	imes 10^{-3} \% = \frac{5 	imes 10^{-3}}{100} = 5 	imes 10^{-5}$.Substituting these values,$\beta = \frac{10^5}{5 	imes 10^{-5}} = 0.2 	imes 10^{10} = 2 	imes 10^9 \, Pa$.The speed of sound $v$ in a fluid is given by $v = \sqrt{\frac{\beta}{ho}}$,where $ho = 10^3 \, kg/m^3$.$v = \sqrt{\frac{2 	imes 10^9}{10^3}} = \sqrt{2 	imes 10^6} = 1000 \sqrt{2} \approx 1414 \, m/s$.

It is found that an increase in pressure of $100 \, kPa$ causes a certain volume of water to decrease by $5 \times 10^{-3}$ percent of its original volume. Then the speed of sound in the water is about .... $m/s$ (density of water $10^3 \, kg/m^3$)

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