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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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Transcript of Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T...
![Page 1: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/1.jpg)
Sound
and the Doppler effectand the Doppler effect
![Page 2: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/2.jpg)
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
![Page 3: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/3.jpg)
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
![Page 4: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/4.jpg)
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
![Page 5: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/5.jpg)
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
![Page 6: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/6.jpg)
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)
![Page 7: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/7.jpg)
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.
![Page 8: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/8.jpg)
The Doppler effect
• Passing Train
• Doppler applet
• Doppler2
![Page 9: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/9.jpg)
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)
![Page 10: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/10.jpg)
• 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.
![Page 11: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/11.jpg)
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
![Page 12: Sound and the Doppler effect. L7 c1 In general the velocity of a wave is a. f/T T=tension b. λ/T T=period c. 2 π/ω d. 2 π/k e. ωt.](https://reader030.fdocuments.in/reader030/viewer/2022020319/56649f335503460f94c50789/html5/thumbnails/12.jpg)
Ultrasound
f=3Hz water~0.5 mm
10 wks
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2
12
F=-kx x=Acos( t+ )
1
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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