review for chapters 15-17 fall 2014 - university of alabama at …mirov/review for chapters...
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Review for Chapters 15-17Oscillations, Waves-I, Waves-II
PH221-2AFall 2014
1. Simple harmonic motion: 2cos( ); sin( ); cos( )m m mx x t v x t a x t
2. The Linear Oscillator: , 2k mTm k
3. Pendulums:
2 , torsion pendulum
L2 , simple pendulum
2 , physical pendulum
ITk
Tg
ITmgh
4. Damped Harmonic Motion: 2
222
1( ) cos( ' ), ' , ( )4 2
bt btm m
m mk bx t x e t E t kx em m
2
1. Sinusoidal waves: 2 1( , ) s i n ( ) , , ,
2 my x t y k x t k f v fT k T
2. Wave speed on stretched string: v
3. Average power transmitted by a sinusoidal wave on a stretched string: 2 212a v g mP v y
4. Interference of waves: 1 1' ( , ) [ 2 c o s ] s i n ( )2 2my x t y k x t
5. Standing waves: ' ( , ) [ 2 s i n ] c o smy x t y k x t
6. Resonance: , f o r 1 , 2 , 3 , . . .2
v vf n nL
7. Sound waves: ,Bv
8. Interference: 2 ( 2 ) f o r 0 , 1 , 2 , 3 . . . , c o n s t r u c t i v e i n t e r f e r e n c e
2 ( 2 1 ) f o r 0 , 1 , 2 , 3 . . . , d e s t r u c t i v e i n t e r f e r e n c e
L m m
L m m
9. Sound Intensity: 2 22
1, , 2 4
sm
P PI I v s IA r
10. Sound level in decibels: 1 2 2( 1 0 ) l o g , 1 0 /oo
Id B I W mI
11. Standing wave patterns in pipes:
, 1 , 2 , 3 , . . . , f o r p i p e o p e n e d f r o m b o t h e n d s2
, 1 , 3 , 5 , . . . , f o r p i p e c l o s e d a t o n e e n d a n d o p e n e d a t t h e o t h e r4
v n vf nL
v n vf nL
12. Beats: 1 2b e a tf f f
3
1. The Doppler effect: f f vv
R
s
' ( ) 1 , vR the speed of the receiver; vs the speed of the
sound;(vs=331m/s); + for receiver approaching stationary emitter, - for receiver moving away from the stationary emitter;
f f vv
Es
'
1
1, vE the speed of the emitter, vs the speed of the sound,
- for emitter approaching stationary receiver, + for emitter moving away from the stationary receiver;
' general Doppler Effects R
s E
v vf fv v
4
5
2. Your grandfather clock’s pendulum has a length of 0.9930 m. if the clock loses half a minute per day, how should you adjust the length of the pendulum?
1
2
2
2
1 1
For a simple pendulum 2
Suppose clock's pendulum oscillates "n" times in a day.(24 3600 30) 86370
after the adjustment of the pendulum's length(24 3600) 86400
2Take ratio
2
LTg
nT s
nT s
LgT L
T Lg
2
1
2
2 2
42 1
8640086370
86400 0.9930 0.9937863700.9937 0.9930 7 10
L
L
L L m
6
7
4.
8
5.
9
6.
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