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 ...
I know that it is an open-closed system, but how would we take into account the amplitude, which is the radius given for this question?
To find the resonant frequency of a well, we need to consider the fundamental frequency, which is also the first resonant frequency. The fundamental frequency is determined by the length of the well, not the amplitude.
The resonant frequencies of a well with an open-closed system are given by the formula:
f = (n * V) / (2πL)
Where:
- f is the resonant frequency
- n is the mode number (1, 2, 3, ...)
- V is the speed of sound in air (approximately 343 m/s)
- L is the length of the well
In this case, the length of the well is the depth, which is given as 5.0 m. We need to find the fifth resonant frequency, so n = 5.
f = (5 * 343) / (2π * 5)
Now we can calculate the resonant frequency.