Physics218 - Feb13

# Physics218 - Feb13 - Physics 218 Honors Waves and Thermal...

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Unformatted text preview: Physics 218 Honors Waves and Thermal Physics, Cornell University Notes for 13 February, 2008 Sound Waves : P ( x,t ) = P + p ( x,t ) excess pressure ; ρ ( x,t ) = ρ + ρ d ( x,t ) ; V ( x,t ) = V + v ( x,t ) . Watching a xed mass of gas : ρ d ( x,t ) ∝ - ρ dη dx (1) We then look at the force on the mass. F s ( x,t )- F s ( x- Δ x,t ) = ma . Pressure = P = F S . So, S [ p ( x,t )- P ( x + Δ x,t )] = S · Δ x · ρ · ∂ 2 η dt 2 . We then have- S · Δ x ∂P dx = S · Δ x · ρ ∂ 2 η ∂t 2 which then provides:- ∂P ∂x = ρ ∂ 2 η ∂t 2 . This means that- ∂p ∂x = ρ ∂ 2 η ∂t 2 (2) The next step is then to relate the pressure p with the excess density ρ d . We now introduce the bulk modulus B which is analogous to Y (young's modulus). [ B ] = N m 2 . Values of B are about ∼ 10 10 N m 2 for solids. B ≡ - dP ( dv v ) ; with dP =- B ( dV V ) (the strict de nition). We can also de ne B as B ≡ - dP dV V =- V dP dV =- V Δ P Δ V =- V p ( x,t ) v ( x,t ) =...
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## 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.

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Physics218 - Feb13 - Physics 218 Honors Waves and Thermal...

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