1. Oscillating pressure: Suppose a travelling sound wave exerts a pressure AP(t) = AP1 COS(27Tf1t) at your eardrum surface. For simplicity, assume your eardrum is circular with a diameter of 10 mm, and that it absorbs all incident energy (nothing is reected). (a) (b) Intensity from pressure amplitude: What is the intensity of sound landing on the eardrum? Power from intensity: \"(hat is the power 9 (\"9\" to distinguish from pressure P) delivered to the ear drum? Force from pressure: What is the force amplitude applied to the eardrum? Power and energy: How much energy is absorbed by the eardrum per oscillation? Note this is also the (integrated) \"work done\" by the above force per cycle. Math enthusiasts can check that the integral this gives the same answer as this simple calculation. ;) Work, force, and displacement: \"Tithout doing any fancy integrals or solving differential equations, let's just get a sense of scale for eardrum motion by asking the following: Suppose a constant force of the above amplitude is applied for half a period and the eardrum moves a distance Ass during this time; in half a period, the work done is AE/Z. How far did the eardrum move? (Just use symbols for now.) Seemingly absurd numbers: At the most sensitive frequency (~ 3 kHz), the minimum intensity we can hear is supposedly about Imin = 1 pVV'IE'mQ. Using (e), how far does the eardrum move, roughly? How does this distance compare to the diameter of an atom? Bonus (worth more than the usual bonuses): Do a better calculation, explain the shortcomings of the above model, and provide a better estimate. Hint: I believe you will want to model the eardrum as a heavily damped harmonic oscillator, likely with a fundamental resonance frequency of "'3 kHz, where there is a minimum in sensitivity (though you could approximate it as having a very high resonance frequency ~40 kHz; to work in the simpler regime). I am happy to help with this because it's a cool problem. .)