physics 231 lecture 34: oscillations & waves
DESCRIPTION
PHYSICS 231 Lecture 34: Oscillations & Waves . Period T 6 3 2 Frequency f 1/6 1/3 ½ (m/k) 6/(2) 3/(2) 2/(2) (2)/6 (2)/3 (2)/2 . Remco Zegers Question hours: Thursday 12:00-13:00 & 17:15-18:15 Helproom. Harmonic oscillations vs circular motion. v 0. t=0. t=1. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/1.jpg)
PHY 2311
PHYSICS 231Lecture 34: Oscillations & Waves
Remco ZegersQuestion hours: Thursday 12:00-13:00 & 17:15-
18:15Helproom
Period T 6 3 2Frequency f 1/6 1/3 ½(m/k) 6/(2) 3/(2) 2/(2) (2)/6 (2)/3 (2)/2
km
fT
221
![Page 2: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/2.jpg)
PHY 2312
Harmonic oscillations vs circular motiont=0 t=1 t=2
t=3 t=4
v0=r=A
v0
=t=t
A
v0
vx
![Page 3: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/3.jpg)
PHY 2313
time (s)
A
-A
-kA/m
kA/m
velocity v
a
x
A(k/m)
-A(k/m)
xharmonic(t)=Acos(t)
vharmonic(t)=-Asin(t)
aharmonic(t)=-2Acos(t)
=2f=2/T=(k/m)
![Page 4: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/4.jpg)
PHY 2314
Another simple harmonic oscillation: the pendulum
Restoring force: F=-mgsinThe force pushes the mass mback to the central position.
sin if is small (<150) radians!!!
F=-mg also =s/Lso: F=-(mg/L)s
![Page 5: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/5.jpg)
PHY 2315
pendulum vs spring
parameter spring pendulum
restoring force F
F=-kx F=-(mg/L)s
period T T=2(m/k) T=2(L/g)*
frequency f f=(k/m)/(2)
f=(g/L)/(2)
angular frequency
=(k/m) =(g/L)
* gL
LmgmT 2/
2
![Page 6: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/6.jpg)
PHY 2316
example: a pendulum clockThe machinery in a pendulum clock is keptin motion by the swinging pendulum.Does the clock run faster, at the same speed,or slower if:a) The mass is hung higherb) The mass is replaced by a heavier massc) The clock is brought to the moond) The clock is put in an upward accelerating
elevator?L m moon elevato
rfaster same slower g
LT 2
![Page 7: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/7.jpg)
PHY 2317
example: the height of the lecture room
demo
22
2
25.04
2
TgTL
gLT
![Page 8: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/8.jpg)
PHY 2318
damped oscillationsIn real life, almost all oscillations eventually stop due to frictional forces. The oscillation is damped. We can alsodamp the oscillation on purpose.
![Page 9: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/9.jpg)
PHY 2319
Types of damping
No dampingsine curve
Under dampingsine curve with decreasingamplitudeCritical dampingOnly one oscillations
Over dampingNever goes through zero
![Page 10: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/10.jpg)
PHY 23110
Waves
The wave carries the disturbance, but not the water
Each point makes a simple harmonic vertical oscillation
position x
position y
![Page 11: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/11.jpg)
PHY 23111
Types of waves
Transversal: movement is perpendicular to the wave motion
waveoscillation
Longitudinal: movement is in the direction of the wave motion
oscillation
![Page 12: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/12.jpg)
PHY 23112
A single pulse
velocity v
time to time t1
x0 x1
v=(x1-x0)/(t1-t0)
![Page 13: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/13.jpg)
PHY 23113
describing a traveling wave
While the wave has traveled onewavelength, each point on the ropehas made one period of oscillation.
v=x/t=/T= f
: wavelengthdistance betweentwo maxima.
![Page 14: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/14.jpg)
PHY 23114
example2m A traveling wave is seen
to have a horizontal distanceof 2m between a maximumand the nearest minimum andvertical height of 2m. If itmoves with 1m/s, what is its:a) amplitudeb) periodc) frequency
2m
a) amplitude: difference between maximum (or minimum) and the equilibrium position in the vertical direction (transversal!) A=2m/2=1mb) v=1m/s, =2*2m=4m T=/v=4/1=4sc) f=1/T=0.25 Hz
![Page 15: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/15.jpg)
PHY 23115
sea wavesAn anchored fishing boat is going up and down with thewaves. It reaches a maximum height every 5 secondsand a person on the boat sees that while reaching a maximum, the previous waves has moves about 40 m awayfrom the boat. What is the speed of the traveling waves?
Period: 5 seconds (time between reaching two maxima)Wavelength: 40 m
v= /T=40/5=8 m/s
![Page 16: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/16.jpg)
PHY 23116
Speed of waves on a string
LM
Fv
/
F tension in the string mass of the string per unit length (meter)
example: violin
L M
screwtension T
v= /T= f=(F/)
so f=(1/)(F/) for fixed wavelength the frequency willgo up (higher tone) if the tension is increased.
![Page 17: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/17.jpg)
PHY 23117
exampleA wave is traveling through thewire with v=24 m/s when thesuspended mass M is 3.0 kg.a) What is the mass per unit length?b) What is v if M=2.0 kg?
a) Tension F=mg=3*9.8=29.4 N v=(F/) so =F/v2=0.05 kg/m b) v=(F/)=(2*9.8/0.05)=19.8 m/s
![Page 18: PHYSICS 231 Lecture 34: Oscillations & Waves](https://reader035.vdocument.in/reader035/viewer/2022062411/568167ab550346895ddcf854/html5/thumbnails/18.jpg)
PHY 23118
bonus ;-)
The block P carries out a simple harmonic motion with f=1.5HzBlock B rests on it and the surface has a coefficient ofstatic friction s=0.60. For what amplitude of the motion doesblock B slip?
The block starts to slip if Ffriction<Fmovementsn-maP=0smg=maP so sg=aP ap= -2Acos(t) so maximally 2A=2fAsg=2fA A= sg/2f=0.62 m