An electronically driven loudspeaker is positioned near the open...

A resonance column apparatus acts as a pipe closed at one end (by the water surface) and open at the other.

The resonant frequencies for a closed pipe are given by:

$f = \dfrac{(2n + 1)v}{4L}$

where $v$ is the speed of sound, $L$ is the length of the air column, and $n = 0, 1, 2, \ldots$

Given $v = 320 \text{ m s}^{-1}$ and $L = 80 \text{ cm} = 0.8 \text{ m}$, we get:

$f = \dfrac{(2n + 1) \times 320}{4 \times 0.8} = 100(2n + 1) \text{ Hz}$

The loudspeaker's frequency range is $20 \text{ Hz}$ to $2000 \text{ Hz}$.

Therefore, $100(2n + 1) \le 2000$

$2n + 1 \le 20$

$n \le 9.5$

Since $n$ must be an integer, the possible values are $n = 0, 1, 2, \ldots, 9$.

The resonant frequencies are $100(2n + 1) \text{ Hz}$, where $n = 0, 1, 2, \ldots, 9$.