THe velocity of sound in air at 16oC is 340$ms^{-1}$. What will it be when the pressure is doubled and its temperature raised to 127ºC?

Analyze the question: We're given the speed of sound at 16°C and asked for its speed at 127°C when the pressure is doubled.

Concept: For an ideal gas, v = √(γP/ρ) = √(γRT/M). Speed depends only on the absolute temperature. Doubling the pressure (with the gas's density adjusting accordingly) does not change the speed, because P/ρ is proportional to T. So:

v₂/v₁ = √(T₂/T₁)

Solution:

Convert to Kelvin:

• T₁ = 16 + 273 = 289 K
• T₂ = 127 + 273 = 400 K

v₂ = 340 × √(400/289) v₂ = 340 × (20/17) v₂ = 20 × 20 = 400 m/s

(Neat: √289 = 17, and 340 = 17 × 20, so the numbers were designed to work out exactly.)

Answer: 400 m/s, which is option A.

Tip: In sound-speed questions, always ignore pressure changes (the density change cancels them out) and convert temperatures to Kelvin. If you see 289 K, think √289 = 17, since JAMB often picks numbers that give perfect squares.