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 metal handrail. The speeds of sound in air, water, and the handrail are 355, 1410, and 5380 m/s, respectively. The sound travels a distance of 140 m in each medium. (a) After the first sound arrives, how much later does the second sound arrive? (b) After the first sound arrives, how much later does the third sound arrive?
t1= s/v1 = 140/355 = 0.394 s.
t2 = s/v2 = 140/1410 = 0.099 s.
t3 =s/v3 = 140/5380 = 0.026 s.
Δt1 =0.099 – 0.026 = 0.073 s.
Δt2 = 0.394 – 0.026 = 0.368 s.
0.073s
0.368s
(a) Well, that's quite a journey for the sound waves! Let's calculate how much later the second sound arrives after the first one, shall we?
To find out, we need to divide the distance traveled by the speed in each medium. So, for the air, since the distance is 140 m and the speed is 355 m/s, the time taken would be 140 m / 355 m/s, which is approximately 0.394 seconds.
Next, in the fresh water, again with a distance of 140 m and a speed of 1410 m/s, the time taken would be 140 m / 1410 m/s, which is about 0.099 seconds.
Therefore, the second sound arrives about 0.394 seconds (the time in air) + 0.099 seconds (the time in water) later than the first sound. Adding those up, we get approximately 0.493 seconds. Ta-da!
(b) Now, let's see how much later the third sound arrives compared to the first one.
Following the same logic, the time taken in the slender metal handrail would be 140 m / 5380 m/s, which is roughly 0.026 seconds.
So, the third sound arrives about 0.394 seconds (the time in air) + 0.099 seconds (the time in water) + 0.026 seconds (the time in the handrail) later than the first sound. Adding those up, we get approximately 0.519 seconds.
And there you have it! The third sound arrives about 0.519 seconds after the first. Keep calm and carry on!
To solve this problem, we'll use the formula Speed = Distance/Time. We'll calculate the time taken by each sound wave to travel a distance of 140 m through each medium.
(a) To determine how later the second sound arrives after the first sound, we need to calculate the time for sound to travel through air and water.
For air:
Speed of sound in air = 355 m/s
Distance traveled in air = 140 m
Using the formula Speed = Distance/Time, we can rearrange it to find Time = Distance/Speed.
Time taken by sound to travel through air = Distance/Speed
= 140 m / 355 m/s
≈ 0.394 s
For water:
Speed of sound in water = 1410 m/s
Distance traveled in water = 140 m
Time taken by sound to travel through water = Distance/Speed
= 140 m / 1410 m/s
≈ 0.099 s
The second sound arrives after the first sound, so the delay is the difference between the two times.
Delay between the arrival of the first and second sounds = Time taken to travel through water - Time taken to travel through air
= 0.099 s - 0.394 s
≈ -0.295 s
The negative sign indicates that the second sound arrives 0.295 seconds earlier than the first sound.
(b) To calculate how much later the third sound arrives after the first sound, we need to calculate the time for sound to travel through air, water, and the handrail.
For the handrail:
Speed of sound in the handrail = 5380 m/s
Distance traveled in the handrail = 140 m
Time taken by sound to travel through the handrail = Distance/Speed
= 140 m / 5380 m/s
≈ 0.026 s
The third sound arrives after the first sound, so the delay is the sum of the times taken to travel through air, water, and the handrail.
Delay between the arrival of the first and third sounds = Time taken to travel through water + Time taken to travel through air + Time taken to travel through the handrail
= 0.099 s + 0.394 s + 0.026 s
≈ 0.519 s
The third sound arrives approximately 0.519 seconds later than the first sound.
To find the time it takes for each sound to travel through the three media, we can use the formula:
Time = Distance / Speed
Let's calculate the time for each medium separately.
(a) To find how much later the second sound arrives after the first sound, we need to calculate the time it takes for sound to travel 140 m in fresh water.
Time = Distance / Speed
Time = 140 m / 1410 m/s
Time = 0.099 seconds
Therefore, the second sound arrives 0.099 seconds later after the first sound.
(b) To find how much later the third sound arrives after the first sound, we need to calculate the time it takes for sound to travel 140 m in the slender metal handrail.
Time = Distance / Speed
Time = 140 m / 5380 m/s
Time = 0.026 seconds
Therefore, the third sound arrives 0.026 seconds later after the first sound.
In summary:
(a) The second sound arrives 0.099 seconds later after the first sound.
(b) The third sound arrives 0.026 seconds later after the first sound.