It is found that an increase in pressure of 1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$1414$

Vedclass · Answer

(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 $10^3 \, kg/m^3$)

Similar Questions

Bulk modulus of water is $2 \times 10^9 \ N/m^2$. The pressure required to increase the volume of water by $0.1 \%$ in $N/m^2$ is:

An increase in pressure required to decrease the $200 \ L$ volume of a liquid by $0.004\%$ in a container is .......... $kPa$ (Bulk modulus of the liquid $= 2100 \ MPa$).

The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$. If $B$ is the Bulk modulus of the metal,the ratio $\frac{\rho^{\prime}}{\rho}$ is:

The bulk modulus of a spherical object is '$B$'. If it is subjected to uniform pressure '$P$',the fractional decrease in radius is

The adiabatic bulk modulus of a gas at a pressure $P$ is (where $\gamma$ is the ratio of specific heat capacities of the gas).

Vedclass Test Series

Exam Paper Generator

Online Exam Module