Oscillations and Waves

Micro-world Macro-world Lect 5

Equilibrium (Fnet = 0)

Examples of unstable Equilibrium

Examples of Stable equilibrium

Destabilizing forces

W

N Fnet = 0

Destabilizing forces

W

N Fnet = away from equil

Destabilizing forces

W

NFnet = away from equil

destabilizing forces always push thesystem further away from equilibrium

W

N

Fnet = 0

restoring forces

W

N

Fnet = toward equil.

restoring forces

W

NFnet = toward equil.

restoring forces

Restoring forces always pushthe system back toward equilibrium

Pendulum

N

W

Mass on a spring

Displacement vs time

amplitude

period (=T)

Displaced systems oscillatearound stable equil. points

Equil. point

Simple harmonic motion

Equil. point

T

T= period = time for 1 complete oscillation

f = frequency = # of oscillations/time = 1/T

Pure Sine-like curve

Masses on springs

Animations courtesy of Dr. Dan Russell, Kettering University

Not all oscillations are nice Sine curves

A

TEquil. point

f=1/T

Natural frequency

f= (1/2)g/l f= (1/2)k/m

Driven oscillators

f = 0.4f0 f = 1.1f0 f = 1.6f0

natural freq. = f0

Resonance (f=f0)

Waves

Animations courtesy of Dr. Dan Russell, Kettering University

Wave in a string

Animations courtesy of Dr. Dan Russell, Kettering University

Pulsed Sound Wave

Harmonic sound wave

Harmonic sound wave

Harmonic wavewavelength

=Wave speed

=v

Wave speed = v =distancetime

wavelengthperiod= =

T

= f

but 1/T=fV=for f=V/

Shake end ofstring up & down

with SHM period = T

Reflection (from a fixed end)

Animations courtesy of Dr. Dan Russell, Kettering University

Reflection (from a loose end)

Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves

pulsed waves

Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves

Wave 1

Wave 2

resultant wave

Two waves in same direction with

slightly different frequencies

“Beats”

Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves

harmonic waves in opposite directions

incident wave

reflected wave

resultant wave

(standing wave)

Animations courtesy of Dr. Dan Russell, Kettering University

Two wave sources

destructive

interference

const

ruct

ive

inte

rfere

nce

Confined waves

Only waves with wavelengths that just fit in survive(all others cancel themselves out)

Confined waves

Allowed frequencies

=(2/3)L

f0=V/ = V/2L

f1=V/ = V/L=2f0

= 2L

=L

=(2/5)L

=L/2

f2=V/=V/(2/3)L=3f0

f3=V/=V/(1/2)L=4f0

f4=V/=V/(2/5)L=5f0

Fundamental tone

1st overtone

3rd overtone

4th overtone

2nd overtone

Ukuleles, etc

L

0 = 2L; f0 = V/2L

1= L; f1 = V/L =2f0

2= 2L/3; f2 = 3f0

3= L/2; f3 = 4f0

Etc…

(V depends on theTension & thickness

Of the string)

Vocal Range – Fundamental Pitch

♩♩

♩♩ ♩♩

♩♩

♩♩

♩♩ ♩♩

♩♩

♩♩

♩♩

♩♩

♩♩

Bass Bass EE22 – E – E44

BaritonBaritone Ge G22 – –

GG44

Tenor Tenor CC22 – C – C55

ContralContraltoDtoD33 – –

DD55

Mezzo-Mezzo-SopranSopranoEoE33 – A – A55

SopranSopranoGoG33 – D – D66

♂♂:: ♀♀::

82 Hz82 Hz

329 329 HzHz

98 Hz98 Hz

392 392 HzHz

131 131 HzHz

523 523 HzHz

147 147 HzHz

587 587 HzHz

165 165 HzHz

880 880 HzHz

196 196 HzHz

1175 1175 HzHz

Thanks to Kristine Ayson

Doppler effect

Wavelength same in all directions

Sound wave stationary source

Wavelength in backward direction is longer (frequency is

lower)

Wavelength in forward direction is shorter (frequency

is higher)

Sound wave moving source

Waves from a stationary source

Wavelength same in all directions

Waves from a moving source

Wavelength in forward direction is shorter (frequency

is higher)

Wavelength in backward direction is longer (frequency is

higher)

v

Visible light

Long wavelengthsShort wavelengths

receding source red-shifted

approaching source blue-shifted

Edwin Hubble

More distant galaxies have bigger red shifts

The universe is expanding!!

Use red- & blue-shifts to study orbital motion of stars in galaxies

receding

red-shifted

approaching

blue-shifted

A typical galactic rotation curve

NGC 6503

Large planets create red-shiftsand blue shifts in the light of their star

Use this to detect planets & measure their orbital frequency

Planetary motion induced stellar velocity