The velocity of sound in air at 15°C is 340ms$^{-1}$. Calculate the velocity at 47$^o$C

Analyze the question: We're given the speed of sound at 15°C and asked for the speed at 47°C. Sound travels faster in warmer air.

Concept: The speed of sound in a gas is proportional to the square root of its absolute (Kelvin) temperature:

v ∝ √T, so v₂/v₁ = √(T₂/T₁)

Solution:

Convert to Kelvin:

• T₁ = 15 + 273 = 288 K
• T₂ = 47 + 273 = 320 K

Apply the formula:

v₂ = v₁ × √(T₂/T₁) v₂ = 340 × √(320/288) v₂ = 340 × √(1.1111) v₂ = 340 × 1.0541 v₂ ≈ 358.4 m/s

Check the options:

• A (790) and B (602) are far too large for a 32°C rise.
• D (322) is lower, but a higher temperature must give a higher speed.
• C (358) matches our result.

Answer: C. 358 m/s

Exam tip: Always convert °C to Kelvin before using v ∝ √T. A quick sanity check: the temperature rises, so the speed must be slightly above 340 m/s. That alone eliminates option D, and the size of the rise eliminates A and B. Also remember that √(320/288) simplifies to √(10/9) = √10/3 ≈ 1.054, which is quick to compute without a calculator.