Speed of sound travel-time puzzle: Two listeners hear the same sound at 5 s and 6 s. Speed of sound = 300 m/s. Find the maximum and minimum possible distances between the two persons. Choose the correct option.
IIT JEE
Physics
Difficulty: Medium
Choose an option
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AMaximum 3300 m; Minimum 300 m
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BMaximum 3000 m; Minimum 0 m
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CMaximum 1800 m; Minimum 1500 m
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DMaximum 3300 m; Minimum 0 m
Answer
Correct Answer: Maximum 3300 m; Minimum 300 m
Explanation
Given
- Speed of sound, v = 300 m/s
- Arrival times: 5 s and 6 s
Step 1: Convert times to distances from sourced1 = v × 5 = 300 × 5 = 1500 md2 = v × 6 = 300 × 6 = 1800 m
Step 2: Use triangle inequality for possible placementsMaximum separation when persons are on opposite sides of the source: dmax = d1 + d2 = 1500 + 1800 = 3300 m.Minimum separation when they are colinear on the same side: dmin = |d2 − d1| = 1800 − 1500 = 300 m.
Final AnswerMaximum 3300 m; Minimum 300 m