A dry water well is 1.5 m in radius and 5.0 m deep.
In order from lowest to highest, the fifth resonant frequency of this well is closest to ...
Question 1 answers
119 Hz
283 Hz
227 Hz
113 Hz
57 Hz
To find the resonant frequency of a well, we need to use the formula:
f = (V / λ) * (1 / 2L)
where:
f = resonant frequency
V = velocity of sound
λ = wavelength
L = depth of the well
First, we need to find the velocity of sound in air, which is approximately 343 m/s.
Next, we need to find the wavelength. The formula for wavelength is:
λ = 2 * π * r
where r is the radius of the well.
λ = 2 * π * 1.5 = 3π
Then, we can substitute the values into the formula:
f = (343 / (3π)) * (1 / (2 * 5))
Simplifying the equation:
f = (343 / (3π)) * (1 / 10)
= (343 / 30π)
Now we can approximate the value of π as 3.14 and calculate:
f ≈ (343 / (30 * 3.14))
≈ 3.63 Hz
Since none of the given answer choices match 3.63 Hz, we need to round the value. The closest option is 4 Hz, but it is not listed. Therefore, none of the provided answer choices are correct.