Ever since seeing the following figure from the previous chapter, you have been fascinated with the hearing response in humans.

A graph shows the sound level $($dB$)$ versus frequency f $($Hz$),$ where the frequency is plotted on a logarithmic scale. The graph is divided into three sections $$ infrasonic frequencies, sonic frequencies, and ultrasonic frequencies. The frequency ranges of numerous sounds with different sound levels are plotted across the three sections.

You have set up an apparatus that allows you to determine your own threshold of hearing as a function of frequency. After performing the experiment and recording the results, you graph the results, which look like the figure below.

A graph shows a curve of sound level $($dB$)$ versus frequency f $($Hz$),$ where the frequency is plotted on a logarithmic scale. The curve begins just around $(10,74)$ and goes down and right linearly before slowly curving more horizontally. Around $(1,100,5),$ the curve is mostly horizontal but then suddenly dips below $0$ dB$,$ hitting a minimum around $3,800$ Hz before rising above $0$ dB again. The curve reaches a peak around $(9,500,18),$ dips again to another minimum around $(11,500,11),$ and then rises once more.

You are intrigued by the two dips in the curve at the right$-$hand side of the graph. You measure carefully and find that the minimum values of these dips occur at $3,800$ Hz and $11,500$ Hz$.$ Performing some online research, you discover that the outer canal of the human ear can be modeled as an air column open at the outer end and closed at the inner end by the eardrum. You use this information to determine the length $($in cm$)$ of the outer canal in your ear. $($Assume that the temperature in your ear canal is $37\mathrm{.}0$C$.$ Assume that the dips occur at the lowest adjacent harmonics.$)$

cm