PS4_03

# PS4_03 - University of Michigan Physics 340 Fall 2003 1...

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University of Michigan Physics 340, Fall 2003 1 October 2003 Reading: Finish French Chap.6. Hirose 5.1-5.5 If you have Serway “Physics for Scientists and Engineers” (3 rd Ed), try Chap. 18 Assignment 4: Coupled Oscillators, Normal Modes Due: Wed Oct 8, in class, or Amidei mailbox by 5pm 1. The Helmholtz Resonator What determines the characteristic frequency when you blow over the top of a bottle? A simple theory, without even appealing to the idea of normal modes was worked out by Helmholtz. The idea is to treat the air in the neck of the bottle as a moving mass, and the air in the bulk of the bottle as a spring. To wit: The neck has cross section A and length L. The bulk has volume 0 V . Take the bulk modulus of air to be 0 Kp γ = , where 0 p is atmospheric pressure. a) Assume that the mass of air in the neck is depressed a small distance x. Write an equation of motion for this mass under the restoring force from the bulk. Show that the air in the neck oscillates with frequency 0 2 s v A f VL π = where s v is the speed of sound.

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## This note was uploaded on 11/08/2009 for the course PHY 245 taught by Professor Barzda during the Spring '09 term at Adelphi.

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PS4_03 - University of Michigan Physics 340 Fall 2003 1...

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