Phys218 - Feb11 - Phys 218 11 February, 2008 - The...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Phys 218 11 February, 2008 - The displacement along the direction of propogation on wave in the x direction. Restoring force due to compression with -density, S - Surface Area, 2 2 Y and the Y - Young's Modulus. F = SY d so since x = v12 2 with v 2 = S . 2 ds dt Waves Through a Rigid Rod: y(x, t) = A exp [i (t - kx + )] = A exp [i (kx - t)] (since cos x = cos -x) Example: Because the forces at x = 0 and x = L are zero, the (x, t) = aei(t-kx) + bei(t-kx) . Because at x = 0: F (o, t) = SY |x=0 = 0. |x=0 = -ik (-a + b) eit = 0 . a = bv . With this we then see that (x, t) = dx dx aeit e-ikv + eikx = 2aeit cos(kx). Now, because at x = L the F = 0, |x=L = 0, then sin(kL) = 0. So we then dx see that kL = n for n N.k = n so that = 2 = 2L . If (x, t) = cn ein t cos (kn x): (for example) L k n So, What is Happening at the lowest mode? (n = 1) kn = n , so n = v = L L d Force Impedance of the Rod: Z = Velocity so since F = SY dx and v = , Z = S Y. Y S L. So, v1 = 1 2 = Y 1 S 2L . Sound Waves: Pressure Waves in Gases: Positive Feedback Mechanism. 1 1. Gas Moves, Density changes 2. Density Changes Pressure Changes 3. Pressure Changes Gas Then Moves, so that the cycle proceeds With P =Pressure, we see that these are true: t=0 P V 0 t=t P +p V +v 0 + So, if x + x + (x + x, t ) is the ending poition of the cylinder, then the mass m = 0 S x = 0 V so that m = (x, t) V (t)= (x, t) S x 1 + x and nally, m = 0 + S x 1 + x so that 0 S x = 0 + S (x, t) 1 + x so, d (x, t) -0 x . 2 ...
View Full Document

This note was uploaded on 02/24/2008 for the course PHYS 2218 taught by Professor Wittich,p during the Spring '08 term at Cornell University (Engineering School).

Page1 / 2

Phys218 - Feb11 - Phys 218 11 February, 2008 - The...

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