Physics Notes

Waves and Optics

Chapters

16-17, 24-26

Wave - the motion of a disturbance that transmits energy

Comparing Types of Waves

1. Mechanical vs Electromagnetic

Mechanical - requires a medium to transfer energy

ie. slinky, water, sound, earthquake

Electromagnetic - requires no medium

ie. radio, micro, IR, visual, UV, X, gamma

3. Transverse vs Longitudinal

Transverse – Particles or disturbance vibrate perpendicularly to the direction of energy transfer

ie. light, slinky

Longitudinal - Particles vibrate parallel to the direction of the energy transfer (Pressure Wave)

compression vs rarefraction

ie. sound, slinky

http://www.phy.ntnu.edu.tw/~hwang/waveType/waveType.html

http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=50

Transverse Waves

Transverse and Longitudinal Waves

Aspects of all SHM (including waves)

Amplitude (A) - maximum displacement from equilibrium (m) Intensity or Energy

Period (T) - time to complete 1 cycle of motion (sec)

Frequency (f) - number of cycles per unit time (Hz)

T = 1 f = 1

f T

More Characteristics of Waves

Crest and Trough- the highest and lowest points from the equilibrium position

Wavelength () - The distance between two adjacent similar points of a periodic wave (m)

Node - Position on a standing wave that has no displacement

Antinode – Position on a standing wave that is displaced to its maximum displacement

Standing Wave – when two waves traveling in opposite directions interfere– The waves must have the same f, A, and – Points of complete constructive and destructive

interference

http://www.phy.ntnu.edu.tw/~hwang/waveType/waveType.html

Standing Waves

How many degrees out of phase are these

2 waves?

Which points are in phase?

In Phase – points on a wave in the same point in their cycle

C and F

90

The Speed of a Wave on a string or spring

V = [F/ (m/L)] ½

The Speed of a Wave

V = d t

Vf = T

f = 1 T

The speed of sound in air is 331 m/sThe speed of light in a vacuum is 3.00 x 108 m/s = c

*Notes from “Activity: Waves and Springs”

What happens to a wave form when there is a disturbance in the medium through which it is traveling???

Standing Waves

Wave interactions

Interference: Constructive

Destructive

Constructive Interference

Destructive Interference

Reflection of a Pulse

SoundSound waves are __________ and ___________.

Pitch - how high or low we perceive sound to be, depending on the frequency of the sound wave

The audible range for humans is 20 Hz to 20,000 Hz.

Ultrasonic waves: Medical applications, animal communication, others...

Speed of sound depends on the medium in which it is traveling in. Speed generally increases with: – denser phase– higher temperature

Sound does not travel in a linear wave as we sometimes model it. It really travels in 3D.

Wave fronts - the concentric spheres of compression radiating from the source of the sound

Doppler Effect - frequency shift that is the result of relative motion between the source of waves and an observer

moving towards f1 = f / (1 - Vs/V)

moving away f1 = f / (1 + Vs/V)

f = emitted frequency

f1 = perceived frequency

V – Velocity of Sound (331 m/s)

Vs – Relative velocity of the Source

Hear the Doppler Effect

Great Physlet

http://webphysics.davidson.edu/applets/applets.html

Click here to see the video of a plane breaking the sound barrier http://www.brewsterschools.org/brewster/brewsterhigh/plamoreaux/assets/sonicboom.mpg

Know Red Shift and Blue Shift

Doppler Effect

Intensity - rate at which energy flows through a unit area perpendicular to the direction of wave motion

intensity = P = P

A 4r2

Decibel Level (dB) - relative intensity of sound (logarithmic relationship)

Natural frequency - certain frequency at which an object vibrates

Resonance - a condition that exists when the frequency of a force applied to a system matches the natural frequency of vibration of the system.

Disastrous effects from earthquakes or windshttp://www.regentsprep.org/Regents/physics/phys04/bresonan/default.htm

Harmonics

fundamental frequency - the lowest frequency of vibration of a standing wave

harmonic series - series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency (overtones)

• Standing wave on a vibrating string

• Pipe open at both ends

• Pipe closed at one end

Beat - interference of waves of slightly different frequencies traveling in the same direction, perceived as a variation in loudnessinterference: constructive and destructive

f beat = (f1 - f2 ) or (f2 - f1 )

Create and Hear Beats: http://explorescience.com/activities/Activity_page.cfm?ActivityID=44

Light waves are __________ and __________.

Electromagnetic Waves –

a transverse wave consisting

of oscillating electric

and magnetic fields

at right angles to

each other

Radio, Micro, IR, light, UV, X, GammaRange of and f

Light

Visible Spectrum ( = 700 nm to 400 nm)

700 nm = 700 x 10-9 m = 7.00 x 10-7 m

Again, a range of colors: ROY G BV

Wave speed

v = f d/t

For light, (c = speed of light = 3.00 x 108 m/s)

c = f

All electromagnetic waves move at the speed of light and behave with the characteristics of light, but they can not be detected by the eye

Light Year – the distance that light travels in a year

d = V x t = 3 x 108 m/s x 1 year

now convert

3 x 108 m x 1 year x 365 days x 24 hours x 3600 s

s 1 year 1 day 1 hour

d = 9.46 x 1015 m

Luminous Flux (P) - the rate at which visible light is emitted from a source.

Unit = lumen (lm) or Watt

Illuminance (E) - the rate at which light falls on a surface

Unit = lux (lx) = lm/m2 or Watt/m2 or candela

E = P = P (sphere)

A 4r2

Luminous –vs- Illuminated

Luminous Intesity (l) – the luminuous flux that falls on an area of 1 m2

Unit – candela or candle power

LASER - a device that produces an intense, nearly parallel beam of coherent light

Light Amplification by Simulated Emission of Radiation

Applications:

Diffraction - the spreading of a wave into a region behind an obstruction

– energy is dispersed

– may result in areas of constructive and destructive interference

– Spectral Emissions and Absorption

Double Slit Diffraction

Maxima – Constructive Interference

d sin m Minima – Destructive Interference

d sin m + ½) m = order of the maxima (0, 1, 2, 3…)

d = distance between slits

Single Slit Diffraction

= d sin d = width of slit

What happens when waves interact with matter?

Reflection - the turning back of waves at the surface of a substance

angle of incidence = angle of reflection

ir

both angles are relative to the normal at the point of contact

virtual image - an image formed by light rays that only appear to intersect

flat mirror-

Mirrors

Convex/Concave

Virtual/Real

Upright/Inverted

Radius of Curvature and Focal Length

Object and Image Distance

Magnification

Mirrors

1 + 1 = 1

so si fMagnification

M = h1 = - si

h so

Mirror Notes and Equations

* Given through “Activity: Concave and Convex Mirrors”

Convex/Concave

Virtual/Real

Upright/Inverted

Radius of Curvature and Focal Length

Object and Image Distance

Magnification

Great Physlethttp://www.phy.ntnu.edu.tw/java/Lens/lens_e.html

Reflection: The color that we perceive an object to be is the color of the light which that object reflects

LASER - a device that produces an intense, nearly parallel beam of coherent light

Light Amplification by Simulated Emission of Radiation

Applications:

Polarization: The alignment of transverse waves in such a way that their vibrations are parallel to each other

-some crystals naturally polarize

-polymers

-double polarization

-applications: reflected glare is generally horizontal

Refraction: The bending of wave disturbance as it passes at an angle from one medium into another

different media result in different speeds of transmission

Index of Refraction (n):

-ratio of speeds of light

n = c

v

The degree of refraction is determined by:

Snell’s Law

n1 (sin 1) = n2(sin 2)

know bending towards or away

As a wave travels from a medium to another velocity and wavelength change, but frequency does not.

n2 = V1 = 1

n1 V2 2

Dispersion – when white light separates into the spectrum of colors- results because different wavelengths travel at different speeds and refract differently

Total Internal Reflection - the complete reflection of light at the boundary of two transparent media; this effect occurs when the angle of incidence exceeds the critical angle

Critical angle

sin c = nr

ni

only when ni > nr

Lens - a transparent object that refracts light rays, causing them to converge or diverge to create an image

converging lenses vs diverging lenses

focal point (f) for a lens is the image distance for an object at an infinite distance

f is: + for converging, - for diverging

Ray Diagrams: 3 reference rays

Is the Image:

Real or Virtual

Upright or Inverted

Enlarged or Smaller

For lenses, the distance equation is similar to that of mirrors

1 + 1 = 1

so si fMagnification

M = h1 = - si

h so

Lenses: • the eye• glasses - combination of lenses

Lens Power

P =1

f

Unit: diopter (D)