i. Will t2 be equal to t1? Justify your answer. ii. Calculate the velocity of sound in both the cases.

Question

Case I: During summer (33 °C), Prakash was waiting for a train at the platform, train arrived tt seconds after he heard train’s whistle.

Case II: During winter (19 °C), train arrived t₂ seconds after Prakash heard the sound of train’s whistle.

i. Will t₂ be equal to t₁? Justify your answer.

ii. Calculate the velocity of sound in both the cases.

(velocity of sound in air at 0 °C = 330 m/s)

Answer 1

i. Velocity of sound is directly proportional to square root of absolute temperature.

Hence, whistle’s sound will be first heard by Prakash in summer than in winter.

Therefore, the time interval between sound and train reaching Prakash in summer will be more than in winter.

i.e., t₁ > t₂

ii. When t = 33 °C

∴ v₁ = v₀ + 0.61t

= 330 + 0.61 × 33

∴ v₁ = 350.13 m/s

When t = 19 °C

v₂ = v₀ + 0.61t

= 330 + 0.61 × 19

v₂ = 341.59 m/s