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Consider a closed box of rigid walls so ...

Consider a closed box of rigid walls so that the density of the air inside it is constant. On heating, the pressure of this enclosed air is increased from `P_0` to P. It is now observed that sound travels 1.5 times faster than at pressure `P_0`. Calculate `P//P_0`

Text Solution

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` v_(p) = sqrt( ( gamma P_0)/( rho))`
` v_(P_0)= sqrt(( gamma P_0)/( rho))`
` V_p = 1.5 V_(P_0)`
` sqrt((gamma P)/( rho) )= 1.5 sqrt((gamma P_0)/( rho))`
`(P )/( rho) = 2.25 (P_0)/(rho)`
` P= 2.25 P_0`
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