IB Ph SL Waves Notes

7/28/2019 IB Ph SL Waves Notes

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IB Physics Waves and Light

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Waves IntroductionA wave is a disturbance in a medium that caries energy without a

net movement of particles.

A wave:

transfers energy. usually involves a periodic, repetitive

movement.

does not result in a net movement of themedium or particles in the medium(mechanical wave).

There are some basic descriptors of a wave.

Wavelength () is distance between anidentical part of the wave.

Amplitude is maximum displacement from

neutral position. This represents the energyof the wave. Greater amplitude carries

greater energy.

Displacement is the position of a particularpoint in the medium as it moves as the wave

passes. Maximum displacement is the amplitude of the wave.

Frequency () is the number of repetitions per second in Hz, s -1

Period (T) is the time for one wavelength to pass a point. T = -1

The velocity (v) of the wave is the speed that a specific part of the

wave passes a point. The speed of a light wave is c.

We will deal with two types of waves:

A transverse wave has the motion of the mediumperpendicular to the movement of the wave pulse.

A longitudinal wave has the motion of the medium parallelto the movement of the wave pulse.

For most waves, the particles of the medium move in a repetitive

way that results in no net displacement.

A transverse wave has the displacement of the particles in themedium moving perpendicular to the direction of the waves

movement


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Examples of transverse waves:

Water waves (ripples of gravity waves, not sound throughwater)

Light waves S-wave earthquake waves Stringed instruments Torsion wave

The high point of a transverse wave is a crest. The low part is a

trough.

A longitudinal wave has the movement of theparticles in the medium in the same dimension

as the direction of movement of the wave.Examples of longitudinal waves:

Sound waved P-type earthquake waves Compression wave

Longitudinal waves create areas of compressionwhere particles are pushed together (higher

density), and rarefaction where particles arepulled apart (lower density)

Sound waves are often represented by a

transverse wave (sinusoidal wave).

Both a transverse and longitudinal wave can be

described with a displacement time graph.Why?

If a single point of the medium is examined over

time, its motion will be periodic.


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The displacement position graph takes apicture of the medium at a specific time.

The displacement is for the medium.The position is for the progress of the

wave. Why does the same graph

describe both types of waves?

As a wave passes a point, the speed of the wave will be measuredby the repeated motion. If the time is measured between two crests

in a wave, the speed is the wavelength divided by the period.

Ex 1:A person is standing on a dock. The person starts a clock as one

crest passes them. As the fifth crest passes, the watch reads 3.5 s.A crest takes 4.7s to pass along the 3.2 m of the dock.

What can you describe quantitatively about the wave?

p. 386, 15, 17, 19, 21pp. 396-398, 44-48, 50, 75, 77, 79, 81, 83

v =

T= f


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Waves One dimensional WavesWe will examine one dimensional waves such as a transverse wave

on a rope or spring, and longitudinal waves on a spring (slinky).

As a mechanical wave reaches the end of its medium, it will

reflect. The energy it contains will not just disappear.

The reflection will vary for a hard (fixed) boundary, and for a soft

(flexible or movable) boundary.

The reflected wave will be upright for a soft boundary, andinverted for a fixed boundary.

A wave that reaches a change in its medium, will be have its speedchanged as it passes into the new medium (refraction), and it will

also reflect at the new medium (a type of boundary).

Traveling into a slower medium is like a hard boundary.Traveling into a faster medium is like a soft boundary.

Watch the speed of the refracted wave, and the nature of the

reflected wave .


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If a continuous wave is moving along a rope, and is reflected, thewave will pass over itself. Two waves at the same point are

combined by the principle of superposition.

Superposition

The displacement of each wave is added together to determine the

displacement of the combined wave.

The two waves are interfering with each other.

Destructive interference occurs if a positive displacement and anegative displacement add together to make a smaller (or zero)

displacement.

Constructive interference occurs if a two displacements that are the

same combine to make a larger displacement.

This applet shows different types of sine waves interfering.

Sketch examples of constructive and destructive interference.


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A reflected wave will interfere with itself and form a specificpattern. This pattern is called a standing wave.

Note the differences between the type of reflection, and the

differences in the standing wave that forms.

Nodes are the points of zero displacement.Anti-nodes are points of maximum displacement.

ExampleRadio waves with a frequency of 188 kHz are received at a house.

The waves then bounce off a mountain behind the house andreflect so that the reception at the house is very poor. What is the

smallest distance that the mountain is from the house?

A standing wave can be created whenever a continuous wave

interferes with another continuous wave of the same frequency andwavelength.

A standing wave is made up of moving waves. The phenomenon

that results looks as if it is standing.

pp. 396-399, 52-57, 67, 68, 84, 87


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Waves Two dimensional wavesTwo dimensional waves behave according to the same rules as one

dimensional waves; however, the applications can be morecomplex.

We will examine water waves initially to discuss two dimensionalwaves.

A two dimensional wave is drawn by showing the wave crestsand/or the direction of the waves motion.

The simplest wave is from a point source.

The wave spreads in all directions radially from the source.

Water waves move in wave fronts. One example of a wavefront is a linear wave.

The activity you are going to complete today will require you to

sketch the ripples in a wave tank in several differentcircumstances.

Water waves propagates more slowly in shallow water.

In an oblique refraction, part of the wave slows before the rest of

the wave. If part of the wave slows, the wave will changedirection.

How can you simulate this with people walking in a line?

Using the waves-tanks, You should diagram the following

situations:1. Reflection at various angles2. Refractions (change depth of water)3. Diffraction past an obstacle on one side with different

wavelengths4. Diffraction of waves around different sized objects (relative

to wavelength).5. Diffraction of waves through different sized opening

(relative to wavelength).


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Huygens PrincipleA linear wave that encounters a change in medium will refract andreflect. Huygens principle can give us a model for the reflected

ray and the refracted ray.This principle is a good model for any type of wave that

encounters a change in medium. We will use this principle forwater waves, and later for light waves.

Huygens can explain why the angle of the incident (incoming)

wave has the same angle as the reflected wave. At an obliqueangle, part of the linear wave hits the barrier before the rest of

the wave.The next diagram has a incoming wave that just hits a barrier

(AA) and the same wave after it has been completely reflected(BB) At first contact, the incident wave moves from A to B.

During that time, the wave at A has moved to B. The speed of

the wave is constant, so:i= r

The wave at point A slows in the new medium. The slow part

moves from A to D as the fast part moves from C to D. These twooccur in the same time.

Velocity in lower medium is less than in the upper medium.

Show that the sine of the incident angle and the refracted angle aredependent on the velocities in those medium.Angles for waves are measured from the normal to the ray thatshows the movement of the wave.

A B =AB

AB B = B A A


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Optics Nature of LightLight is a transverse wave. An electric field and a

magnetic field change orthogonally to the direction ofthe light wave.

The electromagnetic radiation does not require amedium to propagate itself. It can travel through avacuum and many other media. In a vacuum, the speed

of light is a constant, c = 3.00 x 108

m/s.Light will travel slower through different media.

Light waves follow the wave equation:

c = f where c = speed of light.

Light waves with different

frequencies will also havedifferent wavelengths. Theenergy of the photons of

light carry varies withfrequency.

Higher energy light has ahigher frequency and a

shorter wavelength.In the visible part of the

spectrum, violet light hasthe highest energy and

frequency and shortestwavelength. Red light has

the lowest energy andfrequency, and longest

wavelength.

The colours of visible light are a construct of our brain. Differentcells in our retina are sensitive to different colours. By combining

the ratio of inputs from the different cells, the brain generates

colour information.

An emission devise uses combinations of red, green, and blue (rgb)

to produce all the colors.An absorption devise (printer) uses cyan, yellow, magenta and

black (cymk) to produce most of the colors.


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The human eye will interpret equal

amounts of red, green, and blue aswhite.

True white light has equal amounts off

the entire visible spectrum.

pp. 452-453, 33-36, 48-51, 54, 58

Optics ReflectionA light ray that encounters a change in media will: reflect, and/or

refract (pass through), and/or be absorbed.A reflection can occur in an organized way (smooth surface) or in

a random way (rough surface).

Most of the things we see are due to random reflections from roughsurfaces. Some of the light reflected reaches our eye and forms animage in our eye.

A coloured surface will absorb some of the colours and reflect the

colours that we observe.

A reflection from a smooth surface will be organized and producean image.

The key is that the light wave reflects at the same angle that itapproaches the reflector (mirror).

Angles are measured from a line that is normal to the surface of themirror. The incoming ray is the incident ray. The reflected ray is

also measured from the normal to the mirror.

Where would your eye see the object?


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Optics RefractionA light ray that enters a new medium can refract because itchanges its speed in the new medium. The change in speed is

described by the index of refraction (n).

c = speed of light in a vacuumv = velocity of light in medium

This is a specific application of Snells Law for refraction of wavesas they change speed at a boundry.

If the light slows, it will change direction towards the normal. If

the light speeds up, it will change direction away from the normal.

The variables in this relationship can be described bySnells Law.

Angles must be measured from the normal to thesurface.

n is the index of refraction for the media involved.

Example 1:A light ray is moving from crown glass to water with an incident

angle of 35. What is the refracted angle?

Example 2:A surface wave in a liquid changes from 62 to 48 upon traveling

from one liquid into another liquid. What is the relative velocities

of the waves in these two liquids?

p. 509, 67-75 (odd)

n =

c

v

n1sin

1= n

2sin

2


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Diffraction and Interference

Review of diffraction Spreading of a wave as it passes an obstacle or through an

aperture. Opening/barrier is the same order of magnitude as the

wavelength of the wave.

Use of Huygens's Principle can let us visualize the causesof diffraction

Youngs double slit experiment is an application of diffraction andinterference.

This basic principle works for all

wave situations: mechanical waves,light waves, matter waves

(electrons) Waves at the two slits must

be in phase Complex setup in diagram

above

Coherent light (laser) usedfor optical demonstrations.

Frequency and wavelengthdo not change due to thediffraction.

Show why path difference isimportant and the significance of(d + ) and (d +

/2)


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Show how the last relationship isderived if sin =

(for small angles)

Example

A laser is shone through a double slit apparatus with a separationof 0.10 mm onto a screen 2.0 m away. The distance between

bright points on the screen is 1.4 cm. What is the wavelength ofthe laser light?

Why does a diffraction grating break light up into different

colours?

p. 519, # 1-4

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IB Ph SL Waves Notes