Too quiet to hear human senses hearing seeing touch

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Unformatted text preview: ual. ∂s ∂t ￿2 s = smax cos(kx − ω t + φ) 1 = ρ(Area)vsound ω 2 s2 sin2 (kx − ω t + φ) max 2 1 22 I = ρvsound ω smax 2 Monday, October 14, 2013 1 (sin (∗) = ) 2 2 (For point source, s ~ 1/r) Ipoint source = Ps /4π r2 Intensity & sound level −12 β ≡ (10dB ) log10 (I/10 2 W/m ) I = 10−12 W/m2 → β = 0 “What?” Too quiet to hear. Human senses (hearing, seeing, touch, smell, taste) detect intensities I on a log scale. Which is good! Can detect over a large I range, from faint to huge. Conversation has beta about 60dB. Loud rock concert is about 110dB. Pain threshold is about 120dB. Monday, October 14, 2013 Waves in pipes! p (gauge) =0 at open ends s=0 at closed ends So, the wave eqn. BCs are: s|closed = 0 (Just like with a string at fixed end.) Monday, October 14, 2013 and ∂s p = −B ∂x ∂s |open = 0 ∂x (Just like with a string at a free end.) Pipe wave harmonics (Drawing wave’s s displacement. Pressure is ~ derivative, so opposite.) λ = 4L/nodd One end open, one end closed Monday, October 14, 2013 λ = 2L/n Both open, or both closed s & p in pipes Monday, October 14, 2013 The math for pipe wave y z x x=0 s(t, x = 0) = 0 x=L ∂s (t, x = L) = 0 ∂x s = smax sin(kx) cos(kvt + φ0 ) B.C.@L: cos(kL) = 0 k = 2π /λ Monday, October 14, 2013 1 kL = (n + )π 2 L = (2n + 1)λ/4 Math for other cases Both ends closed: B.C.@L: Both ends open: B.C.@L: Monday, October 14, 2013 s = smax sin(kx) cos(kvt + φ) kL = nπ λ = 2L/n s = smax cos(kx) cos(kvt + φ) kL = nπ λ = 2L/n Interference Superpose two traveling wa...
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This note was uploaded on 02/11/2014 for the course PHYSICS 2C taught by Professor Hicks during the Fall '09 term at UCSD.

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