Concepts Of Physics MCQ Edition [Volume 1]PhysicsSound Waves
Determine the temperature at which the speed of sound is twice its value at 0^ C .
Options
- A819^ C
- B1092^ C
- C273^ C
- D546^ C
Correct answer
A. 819^ C
Step-by-step solution
The speed of sound in a gas is given by v = R T M , which implies v T , where T is the absolute temperature. Let v₁ be the speed at T₁ = 0^ C = 273 K and v₂ be the speed at temperature T₂ . Given v₂ = 2v₁ , we have: v₂ v₁ = T₂ T₁ = 2 T₂ T₁ = 4 T₂ = 4T₁ Substituting T₁ = 273 K : T₂ = 4 273 K = 1092 K Converting to Celsius: T₂ = 1092 - 273 = 819^ C