This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the solution to the problem: Given: Distance from the boy to the nearest wall, d_1 = 50 m Time for the first echo (from the nearest wall), t_1 = 0.3 s Time for the second echo (from the farther wall), t_2 = 1.2 s To find: Speed of sound in air, v Distance between the walls, D Step 1: Determine the speed of sound in air (v). The first echo is heard from the nearest wall. The sound travels to the wall and back to the boy. The total distance covered by the sound for the first echo is 2d_1. Using the formula: distance = speed × time. 2d_1 = v × t_1 Substitute the given values: 2 × 50 m = v × 0.3 s 100 m = v × 0.3 s v = 100 m0.3 s v = (1000)/(3) m/s v ≈ 333.33 m/s The speed of sound in air is 333.33 m/s. Step 2: Determine the distance to the farther wall (d_2). The second echo is heard from the farther wall. The sound travels to this wall and back to the boy. The total distance covered by the sound for the second echo is 2d_2. 2d_2 = v × t_2 Substitute the calculated speed of sound and the given time for the second echo: 2d_2 = ((1000)/(3) m/s) × 1.2 s 2d_2 = (1000 × 1.2)/(3) m 2d_2 = (1200)/(3) m 2d_2 = 400 m d_2 = 400 m2 d_2 = 200 m Step 3: Determine the distance between the walls (D). The boy is standing between the two walls. The total distance between the walls is the sum of the distance from the boy to the nearest wall (d_1) and the distance from the boy to the farther wall (d_2). D = d_1 + d_2 D = 50 m + 200 m D = 250 m The distance between the walls is 250 m.