# hw07 - MIT OpenCourseWare http://ocw.mit.edu 6.055J /...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.055J/2.038J (Spring 2008) Homework 7 The following problems are for your enjoyment. Happy estimating! Easier 1. Perfume If the diffusion constant (in air) for small perfume molecules is 10 6 m 2 s 1 , estimate the time for perfume molecules to diffuse across a room. Now try the experiment: How long does it take to smell the perfume from across the room? Explain the large discrepancy between the theoretical estimate and the experimental value. 2. Semitones Estimate 1 . 5 14 using semitones and compare with the exact value. 3. Blackbody temperature of the earth The earths surface temperature is mostly due to solar radiation. The solar ux S 1350 W m 2 is the amount of solar energy reaching the top of the earths atmosphere. But that energy is spread over the surface of a sphere, so S / 4 is the relevant ux for calculating the surface temperature. Some of that energy is reected back to space by clouds or ocean before it can heat the ground, so the heating ux is slightly lower than S / 4. A useful estimate is S 250 W m 2 . Look up the StefanBoltzmann law (or see Problem 7 ) and use it to find the blackbody tem- perature of the earth. Your value should be close to room temperature but enough colder to make you wonder about the discrepancy. Why is the actual average surface temperature warmer than the value calcu- lated in this problem? 4. Xylophone notes If you double the width, thickness, and length of a xylophone slat, what do you do to the frequency of the note that it makes?...
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.

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hw07 - MIT OpenCourseWare http://ocw.mit.edu 6.055J /...

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