To solve this problem, we need to calculate the time it takes for the sound to travel through each medium using the formula:
Time = Distance / Speed
(a) To find the time it takes for the sound to travel through water and reach the other end of the pier, we can use the speed of sound in water (1460 m/s) and the distance traveled in water (166 m).
Time in water = 166 m / 1460 m/s = 0.11369863 s
Since the second sound does not need to travel through air, we do not need to calculate the time it takes for the sound to travel through air.
(b) To find the time it takes for the sound to travel through the slender metal handrail and reach the other end of the pier, we can use the speed of sound in the handrail (5400 m/s) and the distance traveled in the handrail (166 m).
Time in handrail = 166 m / 5400 m/s = 0.03074074 s
To find the time difference between the first and second sound arrivals, we subtract the time for the first sound from the time for the second sound:
Time difference = Time in water - Time in air = 0.11369863 s
To find the time difference between the first and third sound arrivals, we subtract the time for the first sound from the time for the third sound:
Time difference = Time in handrail - Time in air = 0.03074074 s
Therefore, (a) the second sound arrives approximately 0.1137 seconds later after the first sound, and (b) the third sound arrives approximately 0.0307 seconds later after the first sound.