On a winter day, a student in the laboratory measures the speed of sound to be 340 m s ⁻¹ when the room temperature is 17^ C . Determine the speed that will be measured by another student performing the same experiment on a day when the room temperature is 32^ C .

Step-by-step solution

The speed of sound in a gas is directly proportional to the square root of its absolute temperature, v T . Given v₁ = 340 m s ⁻¹ at T₁ = 17^ C = 17 + 273 = 290 K . We need to find the speed v₂ at T₂ = 32^ C = 32 + 273 = 305 K . Using the relation v₂ v₁ = T₂ T₁ : v₂ = 340 305 290 v₂ = 340 61 58 v₂ 340 1.0255 348.7 m s ⁻¹ Rounding to the nearest integer gives 349 m s ⁻¹ .