Determine the change in volume of 6 litres of alcohol if the pressure is decreased from 200 cm of Hg to 75 cm. [velocity of sound in alcohol us 1280 m/s, density of alcohol = 0.81 gm/c c, density of Hg `- 13.6 gm//c c` and `g = 9.81 m//s^(2)`]

Explanation

For propagation of sound in liquid `v = sqrt((B//rho))` i.e., `B = v^(2)rho` But by definition `B=-V(DeltaP)/(DeltaV)`
So `-V(Delta P)/(DeltaV)=v^(2)rho`, i.e., `Delta V=(V(-DeltaP))/(rhov^(2))`
Here ` DeltaP=H_(2)rhog-H_(1)rhog=(750-200)xx13.6 xx981=-1.667 xx 10^(6) "dynes/cm"^(2)`
So `DeltaV=((6xx10^(3))(1.667xx10^(6)))/(0.81xx(1.280xx10^(5))^(2))=0.75c c`.