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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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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