sound and the doppler effect. l7 c1 in general the velocity of a wave is a. f/t t=tension b. λ/t...
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Sound
and the Doppler effectand the Doppler effect
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L7 c1
In general the velocity of a wave is
a. f/T T=tension
b. λ/T T=period
c. 2π/ω
d. 2π/k
e. ωt
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SoundSound waves
represent compressions and rarefactions of the
medium
This can be the surface of a
speaker, or your vocal chords
x
Density
or P
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The higer the pressure the
faster the speed of the waves
The denser a medium is the
slower the speed of the
waves
v must grow with P
v must drop with
• P has units of force/area: mass/(length • time2)• has units of mass /length3
The only combination that has units of speed is:
P
cv These arguments determine
v up to a numerical constant c.
Its value depends on the medium
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13.25
• A sinusoidal sound wave is described by the displacement
D(x,t)=(2m)cos[(15.7m-1)x-(858s-1)t]a) find the amplitude, wavelength and speed of
this waveb) Determine the instantaneous displacement of
an element of air at the position x=0.5 m at t=3ms
c) Determine the maximum speed of an elements oscillatory motion
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Exercise 13.25 I need the general expression for a wave. The rest is plug and chug
-1 -1
sin( )
(2 m)cos 15.7 m 858 s
D A kx t
x t
-1
( ) 2 m = /2
2 2 15.7m m 0.4m
15.7858 m m
54.6515.7 s s
a A
k
vk
( ) x 0.05m, 0.003s
(2 m)cos 15.7 0.05 858 0.003
1.95 m
b t
D
-1( ) A cos( ) A 858 s (2 m) 0.0017m/sdD
c kx tdt
remembercos=sin(+/2)
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L7 c2) All mechanical waves require
a. some source of disturbance.
b. a medium that can be disturbed.
c. a physical mechanism through which particles of the medium can exert forces on one another.
d. all of the above.
e. only (a) and (b) above.
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The Doppler effect
• Passing Train
• Doppler applet
• Doppler2
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General Doppler Formula
LL S
S
v vf f
v v
fs= frequency emitted by source vS=Velocity of source
fL= frequency received by listener vL=Velocity of listener
positive direction is from L to S so fL>fS when they are moving toward each other
SSourceLListener
+
vs (negative) vL (positive)
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• L7 C3) The Doppler effect causes the sound from a source moving toward an observer to appear to have a
a. greater amplitude.
b. smaller amplitude.
c. greater speed.
d. lower frequency.
e. higher frequency.
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Example
Example: Police car w/ siren and passenger car approaching each other; both moving.fsiren = 250 Hz vs = 27 m/s (60 mph) vL = 27 m/s
f (250)330 27
330 27
295 Hz
Once they pass each other and are moving away
f (250)330 27330 27
213 Hz
LL S
S
v vf f
v v
fs= frequency emitted by source vS=Velocity of source
fL= frequency received by listener vL=Velocity of listener
positive direction is from L to S so fL>fS when they are moving toward each other
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Ultrasound
f=3Hz water~0.5 mm
10 wks
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2
12
F=-kx x=Acos( t+ )
1
2spring
f fT
kSHO
m
gPendulum
L
PE kx Energy PE KE
total 0
0
2 2 2 20
2 20
sin( )
/
( / ) ( )
/tan
ma F kx bv F t
F mA
b m
b m
2
)2/(
2
)cos(
m
b
m
k
tAex tmb
/0
t mE E e where
b
( , ) sin( )
2
D x t A kx t
k vk
dampled SHO
driven and dampled SHO
traveling waves
2 2
2 2 2
1d d
dt c dx
E E
8
0 0
13 10 m/sc
0
0
0 0
cos( )
cos( )
E kx t
B kx t
E cB
E x
B z
^
^
2av 0 0
1
2u E
0
1S E B
2
0 0
~ /EB E
Power areac
S
20
02avg
EPowerI S
Area c p=E/c
1 1 / 1 PowerP
F p E c I
A A t A t A c c
I=I0 cos2
LL S
S
v vf f
v v
positive direction is from L to S