Question:

Two friends are standing along a steel fence at a distance of 340 m from each other as shown in fig. Gunjan places her ear over the fence and her friend knocks the fence with a metal object. Using the values of the speed of sound in steel and air given in above Table, calculate the time difference between the sound that reached Gunjan through the air and the steel. Would it have been possible for her to distinguish between the two sounds? (The time interval between two sounds must be at least 0.1s to be heard separately.) [Pg. No. 135]

Answer: Verified

Distance between the two friends = 340 m

Speed of sound in air = 340 m s⁻¹

Speed of sound in steel = 5000 m s⁻¹

Time taken through air,

$t = \frac{d}{v}$

$= \frac{340}{340} = 1 \text{ s}$

Time taken through steel,

$t = \frac{340}{5000}$

$= 0.068 \text{ s}$

Time difference, 1 - 0.068 = 0.932 s

So, the sound travelling through steel reaches Gunjan about 0.932 s earlier than the sound travelling through air. Since this time difference is much greater than 0.1 s, Gunjan would be able to distinguish the two sounds separately.

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