phy 113 a general physics i 9-9:50 am mwf olin 101 plan...
TRANSCRIPT
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 1
PHY 113 A General Physics I9-9:50 AM MWF Olin 101
Plan for Lecture 35:Chapter 17 & 18 – Physics of wave motion
1. Standing waves 2. Sound waves3. Doppler effect
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 2
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 3
ftxytxyftxytxy leftright λ
π2sin),(λ
π2sin),( 00
ftxytxtxy leftright π2cosλπ2sin2),(y),( 0
“Standing” wave:
Combinations of waves (“superposition”)
BABABA 21
21 cossin2sinsin
: thatNote
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 4
ftxytxtxy leftright π2cosλπ2sin2),(y),( 0
“Standing” wave:
iclicker exercise:Why is this superposition result important?
A. Physics instructors like to torture their students.B. While the trigonometric relation is always true, it
is rarely useful for describing real situations.C. It can describe the motion of a guitar string.
BABABA 21
21 cossin2sinsin
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 5
cλiffsatisfiedEquality
0λπ2π2π2cos
λπ2sin
π2cosλπ2sin
λπ2:Check
π2cosλπ2sinπ2:Check
π2cosλπ2sin),(
0:equation wave the tosolutions waveStanding
222
2
22
2
2
2
2standing
2
22
standing2
standing
2
22
2
2
f
cfftxAxyc
ty
ftxAxy
ftxAfty
ftxAtxy
xyc
ty
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 6
.....4,3,2,12
2sin:shapesspatialPossible
nLπnxA
...........4,3,2,12
2
2cos2sin:form waveStanding
nLncf
nL
πftπxA
nn
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 7
iclicker question:Which of the following statements are true about the string motions described above?
A. The human ear can directly hear the string vibrations.
B. The human ear could only hear the string vibration if it occurs in vacuum.
C. The human ear can only hear the string vibration if it produces a sound wave in air.
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 8
Comments about waves in materials: Solid materials can support both transverse
and longitudinal wave motion Fluids, especially gases can support only
longitudinal wave motion
0
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ct
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 9
Standing waves in air:
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 10
Coupling standing wave resonances in materials with sound:
iclicker question:Suppose an “A” is played on a guitar string. The standing wave on the string has a frequency (fg), wavelength (g) and speed (cg) . Which properties of the resultant sound wave are the same as wave on the guitar string?
A. Frequency fsB. Wavelength sC. Speed csD. A-CE. None of these
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 11
coupling tosound
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 12
The “Doppler” effect v=sound velocity
observer moving, source stationary
source
observer
vS=0
OO
O
O
vvvT
ftt
tvdTtvtvdvt
112
22
11
vvvff O
SO
d
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 13
The “Doppler” effect v=sound velocity
observer stationary, source moving
vvvT
ftt
dTvTtvdvt
S
O
S
112
2
1
d
SSO vvvff
toward
awayS
OSO vv
vvff
:Summary
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 14
Example:
S
OSO vv
vvff
toward
awayS
OSO vv
vvff
:caseIn this
SOSO vvff Velocity of sound:
v = 343 m/s m/s40)( S
OSO ffvvvv
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 15
iclicker question
Is Doppler radar described by the equations given above for sound Doppler?
(A)yes (B) no
Is “ultra sound” subject to the sound form of the Doppler effect?
(A) yes (B) no
12/03/2012 PHY 113 A Fall 2012 -- Lecture 35 16
S
OSO vv
vvff
:effectDoppler soundofSummary toward
away
R
RSO vv
vvff
: wavesneticelectromagfor effect Doppler Relative velocity of source toward observer