What is the velocity of sound at 100 oC if the velocity of sound at 0 oC is 340ms -1?

Analyze the question: We need the speed of sound at 100 °C, given 340 m/s at 0 °C. The speed of sound in a gas depends on the absolute temperature.

Concept: v ∝ √T, where T is in kelvin. So

v₂/v₁ = √(T₂/T₁)

Solution:

• T₁ = 0 °C = 273 K
• T₂ = 100 °C = 373 K
• v₁ = 340 m/s

v₂ = 340 × √(373/273)

373/273 ≈ 1.3663

√1.3663 ≈ 1.1689

v₂ ≈ 340 × 1.1689 ≈ 397.4 m/s

Answer: v ≈ 397 m/s, which is option C.

(Note: the options are written as "m⁻¹", but the unit should be m s⁻¹. This is just a typing error in the question.)

Tip: Always convert temperature to kelvin before using v ∝ √T. A common mistake is using 0 and 100 directly, which gives nonsense. Also, as a quick check, the speed should rise by about 0.6 m/s per °C, so 340 + 60 ≈ 400 m/s, which points to 397 and rules out A, B and D.