1

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.