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:
sclosed = 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.
 Fall '09
 Hicks

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