Displacement wave equation multiply both sides of the

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Unformatted text preview: ≤ 60, 000Hz Cats: 60Hz ≤ f ≤ 80, 000Hz Bats: 10, 000Hz ≤ f ≤ 200, 000Hz Dolphin: Monday, October 14, 2013 75Hz ≤ f ≤ 150, 000Hz Piano Monday, October 14, 2013 Pressure Wave eqn. Displacement wave equation: Multiply both sides of the s wave eqn. by ∂ ·B ∂x So get same wave eqn for pressure 1 ∂2s ∂2s =2 2 ∂ x2 v ∂t (Derived a few slides ago.) ∂s p = −B ∂x 1 ∂2p ∂2p =2 2 ∂ x2 v ∂t s(x, t) = A cos(k (x − vt) + φ0 ) p(x, t) = BkA sin(k (x − vt) + φ0 ) pmax = BkA = (v ρ)(Aω ) Monday, October 14, 2013 Larger A (louder) or higher frequency gives bigger p, this can hurt your ears! Ouch! s(x, t) = A cos(k (x − vt) + φ0 ) p(x, t) = BkA sin(k (x − vt) + φ0 ) pmax = BkA = (v ρ)(Aω ) Larger A (louder) or higher frequency gives bigger p, this can hurt your ears! Largest gauge pressure before damaging your ears: pmax ≈ 28P a v ≈ 343m/s ρair ≈ 1.21kg/m3 (Aω )max ≈ 28/(343)(1.21) ≈ 0.067m/s 3 e.g. f = 10 Hz = ω /2π Amax ≈ 1.1 × 10−5 m Sound wave amplitude, at this frequency, should be less, or you’ll damage your ears. Monday, October 14, 2013 Intensity Power I= Area Line on top means “average”, sometimes we also use these brackets < > to denote averaging. dE dK dU dK (Area). I = = + =2 dt dt dt dt dK 1 dm = dt 2 dt ￿ ∂s ∂t ￿2 1 dx = ρArea 2 dt ￿ Like the harmonic oscillator, all oscillating systems have average K and U are eq...
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