ps05 - ASSIGNMENT 5 Physics 218 Due Friday October 1 Fall...

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ASSIGNMENT 5 Physics 218 Due Friday October 1 Fall 2004 1. A singer in the Metropolitan Opera needs to hold a certain note at a sound level of 80 dB (dynamical level approximately ff or fortissimo) for 1 s. Acoustics of concert halls is very complicated and the reflections from all surfaces in the auditorium (including the members of the audience) are very important elements in determining what is heard. However, we can get some idea of the sound energy produced by the singer if we ignore these complications and calculate intensities in two extreme approximations – the sound wave has uniform intensity in the whole volume of the opera house, or the sound intensity varies as 1 /r 2 where r is the distance from the singer (as in a spherical wave). The Metropolitan Opera house is very roughly a cube with lengths of the sides d = 30 m. (The actual volume is about 25,000 m 3 instead of 27,000 m 3 .) We can think of the stage as centered in one side of the cube at the level of the bottom surface of the cube. (a) Assume that the sound intensity is uniform at a level I = 80 dB throughout the volume. Then calculate the power P u passing through an area S = d 2 and the energy E u that passes through the area in t = 1 s. (b) Now assume that the singer radiates the sound uniformly in 1 4 of the volume (or area) of the sphere and that the sound is perfectly absorbed when it hits any surface. Then
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