## [answered] B1 A model for the vibrations of a wine glass is 513+Ai:+w2

B1 A model for the vibrations of a wine glass is 513+Ai:+w2x=0 where A and w are constants. Suppose that when struck the wine glass vibrates at 660 Hz (about the second E above middle C on a piano). Show that \/ 4w2 ? A2 = 26407r If it takes about 3 seconds for the sound to die away, and this happens when the original vibrations have reduced to 1/100 of their original level, show that _ 2 log 100 _ ?3 , and hence that A = 3.07 and w = 4.15 X 103 (both to three signi?cant ?gures). A The glass can stand deforming only to a: z 1. A pure tone at 660 Hz is pro? duced at D decibels and aimed at the glass, forcing it at its natural frequency, so that the vibrations are now modelled by .. - 2 10(D/10)?8 a: + Ax + w a: = T cos(13207rt).
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