The enclosed air inside a closed box of rigid walls has pressure P₁ . The density of air inside this box is constant. On heating the gas, the pressure of the enclosed air is increased from P₁ to P₂ . Now it is observed that the sound travels 1.4 times faster than at pressure P₁ . The ratio P₂ by P₁ is

Step-by-step solution

The speed of sound in a gas is given by v = P . Since the box has rigid walls, the volume is constant. The mass of the enclosed air is also constant, which means the density remains constant. Thus, the speed of sound is directly proportional to the square root of pressure, v P . v₂ v₁ = P₂ P₁ Given that v₂ = 1.4 v₁ , we have: 1.4 = P₂ P₁ Squaring both sides gives: P₂ P₁ = (1.4)^2 = 1.96 Answer: 1.96