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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online