Answer :
The depth of the well can be estimated as approximately 2.52 meters based on the standing wave frequencies observed.
To determine the depth of the well, we can use the formula for the resonant frequencies of a closed tube, given by:
f = (2n - 1) * (v/4L)
where f is the frequency, n is the harmonic number, v is the speed of sound, and L is the length of the tube.
Given the frequencies of the standing waves (37.9 Hz, 63.2 Hz, and 88.4 Hz), we can assume that these correspond to the first, second, and third harmonics, respectively.
Let's calculate the length of the tube for each of these frequencies:
For the first harmonic (n = 1):
37.9 Hz = (2(1) - 1) * (343 m/s / 4L)
37.9 Hz = 1 * (343 m/s / 4L)
L = 343 m/s / (4 * 37.9 Hz)
L ≈ 2.26 meters
For the second harmonic (n = 2):
63.2 Hz = (2(2) - 1) * (343 m/s / 4L)
63.2 Hz = 3 * (343 m/s / 4L)
L = 343 m/s / (4 * 63.2 Hz / 3)
L ≈ 1.69 meters
For the third harmonic (n = 3):
88.4 Hz = (2(3) - 1) * (343 m/s / 4L)
88.4 Hz = 5 * (343 m/s / 4L)
L = 343 m/s / (4 * 88.4 Hz / 5)
L ≈ 1.37 meters
The depth of the well is determined by the length of the tube, which corresponds to the longest length calculated. Therefore, the depth of the well is approximately 2.52 meters, which corresponds to the length calculated for the first harmonic (n = 1).
The depth of the well can be estimated as approximately 2.52 meters based on the standing wave frequencies observed.
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