The human ear canal is$,$ on average, $2\mathrm{.}5$cm$2\mathrm{.}5$cm long and aids in hearing by acting like a resonant cavity that is closed on one end and open on the other. The length of the ear canal is partially responsible for our sensitivities to certain frequencies. Use $340$m$/$s$340$m$/$s for the speed of sound when performing the following calculations.

What is the first resonant frequency?

What is the wavelength at second resonance?

How does the first resonant frequency change if the ear canal is full of water?

At a listener's ear, the intensity of a conversation is $4106$W$/$m$24106$W$/$m$2$ and a typical adult's ear has a surface area of $210103$m$2210103$m$2.$ What is the power of the sound waves on the ear?

Long$-$term exposure to loud noises can damage hearing. If a loud machine produces sounds with an intensity level of $110$dB$110$dB$,$ what would the intensity level be if the intensity were reduced by a factor of $5?$