An explosion occurs at the end of a pier. The sound reaches the other end of the pier by traveling through three media: air, fresh water, and a slender handrail of solid steel. The speeds of sound in air, water, and the handrail are 343, 1482, and 5040 m/s, respectively. The sound travels a distance of 115 m in each medium.

Question

An explosion occurs at the end of a pier. The sound reaches the other end of the pier by traveling through three media: air, fresh water, and a slender handrail of solid steel. The speeds of sound in air, water, and the handrail are 343, 1482, and 5040 m/s, respectively. The sound travels a distance of 115 m in each medium.

Answer 1

To find the total time it takes for the sound to reach the other end of the pier, we need to calculate the time it takes for sound to travel through each medium separately and then add them up.

Step 1: Calculate the time taken for sound to travel through air.
The speed of sound in air is 343 m/s, and the distance traveled is 115 m.
Using the formula: time = distance / speed
time in air = 115 m / 343 m/s = 0.336 s

Step 2: Calculate the time taken for sound to travel through water.
The speed of sound in water is 1482 m/s, and the distance traveled is 115 m.
time in water = 115 m / 1482 m/s = 0.078 s

Step 3: Calculate the time taken for sound to travel through the handrail.
The speed of sound in the handrail is 5040 m/s, and the distance traveled is 115 m.
time in handrail = 115 m / 5040 m/s = 0.023 s

Step 4: Add up the times calculated in steps 1, 2, and 3.
total time = 0.336 s + 0.078 s + 0.023 s = 0.437 s

Therefore, the sound takes a total of 0.437 seconds to reach the other end of the pier.

Answer 2

To calculate the total time taken for the sound to travel through each medium, we need to use the formula:

Time = Distance / Speed

Let's calculate the time taken for the sound to travel through each medium individually:

1. Air:
Distance = 115 m
Speed = 343 m/s
Time = Distance / Speed = 115 m / 343 m/s = 0.335 s

2. Fresh Water:
Distance = 115 m
Speed = 1482 m/s
Time = Distance / Speed = 115 m / 1482 m/s ≈ 0.078 s

3. Solid Steel Handrail:
Distance = 115 m
Speed = 5040 m/s
Time = Distance / Speed = 115 m / 5040 m/s ≈ 0.023 s

Now, to find the total time taken, we need to add up the times for each medium:

Total Time = Time in Air + Time in Water + Time in Steel Handrail
Total Time = 0.335 s + 0.078 s + 0.023 s
Total Time ≈ 0.436 s

Therefore, the total time taken for the sound to travel from the point of explosion to the other end of the pier is approximately 0.436 seconds.