Sight and Sound

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Sight and Sound

• Waves
• Sound
• Light - Geometric Optics

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Waves and Energy Transfer

• This presentation will consider
• Wave Properties
• Wave Interference
• v f ?

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The Measures of a Wave

• The period of a wave is the time needed for the
  motion to repeat itself. Period is measured in
  Seconds.
• Wavelength is the shortest distance between
  points where the wave pattern repeats itself.
• The frequency of the wave is the number of
  complete vibrations per second measured at a
  fixed location. FREQUENCY is measured in Hertz.
• The amplitude of the wave is its maximum
  displacement of the wave from its rest position.

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The physical properties of a wave.
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Types of Waves

• Energy can be transferred by particles or by
  waves.
• Mechanical waves need a medium to travel through.
• In a transverse wave, particles vibrate at right
  angles to the direction of the waves velocity.
• A longitudinal wave causes the particles of a
  medium to move parallel to the direction of the
  wave.

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The speed of a wave.

• The speed,v, of a wave relates the frequency, f,
  of a wave to its wavelength, ?.
• The origin of this formula is in
• The displacement, d, is the distance between two
  crests (or troughs) and time is the period, T, of
  one complete cycle. Of course, the Frequency is
  simply 1/T

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Waves at Boundaries between Media.

• When the medium changes, wave energy is both
  reflected and transmitted.
• Waves passing from one medium into another have
  the same frequency. The wavelength change depends
  on velocity change so that

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Interference of Waves

• The principle of superposition states that the
  displacement of a medium caused by two or more
  waves is the algebraic sum of the displacements
  caused by the individual waves.
• Constructive interference occurs when two waves
  combine to produce a wave with larger amplitude.
• Destructive Interference occurs when two waves
  combine to produce a wave with a smaller
  amplitude.

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Sound
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Properties of Sound Waves

• Sound saves are longitudinal waves
• The speed in air increases 0.6m/s for each oC
  increase.
• Vsound 330 0.6 x T m/sec
• The speed of sound is higher in liquids and
  solids than it is in gases.
• Sound has properties of all other waves
  reflection, refraction, interference,
  diffractions.

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Sound of sound in various materials at 20oC.
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Pitch and Loudness

• Pitch is essentially the frequency of the wave.
  The higher the frequency, the higher the pitch.
• Loudness depends on the amplitude of the pressure
  variation wave. The louder the sound, the bigger
  the amplitude.
• Sound level is measured in decibels (dB).
• Two notes with frequencies related by the ratio
  21 are said to differ by an octave.

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Loudness-level Curves
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Equation for sound intensity

• The intensity level, b, of any sound is defined
  in terms of its intensity, I as follows

NOTE - Io is usually taken as the minimum
intensity level for an average person, which is
Io 1.0 x 10-12 W/m2.
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Some Sound Levels (dB)
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Sources of Sound

• The source of sound is a vibrating object.
• Almost any object can vibrate and hence be a
  source of sound.
• Standing waves are produced and the object
  vibrates at its natural resonant frequency.

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Sources of Sound Vibrating Strings.

• The most widely used instruments are the violin,
  guitar and piano.
• The pitch is normally determined by the lowest
  resonant frequency the fundamental.
• The wavelength,l, of the fundamental is equal to
  twice the length, L, of the string or l 2L.
• The frequency is f v/l v/2L where v is the
  velocity of the wave on the string.
• The stings on a guitar are all the same length
  but have different masses. This affects the
  velocity and hence the frequency of vibration.

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Sources of Sound Vibrating Columns of Air.

• Instruments such as woodwinds produce sound from
  the vibrations of standing waves in a column of
  air within a tube or pipe.
• The simplest mode of vibration is the Fundamental
  mode. Higher harmonics (or overtones) can also
  be produced.
• The frequency of each overtone is an integral
  multiple of the fundamental frequency.

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Interference of Sound Beats.

• When two waves simultaneously pass through the
  same region of space, they interfere with one
  another.
• Beats occur when two sounds of slightly different
  frequency interfere with one another.
• The beat frequency fb is
• fb f2 f1

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The Doppler Effect

• When a source of a sound is moving toward an
  observer, the pitch is higher than when the
  source is at rest and when the source is
  traveling away form the observer, the pitch is
  lower.
• This phenomenon is known as the Doppler Effect.
• This effect occurs for all types of waves.

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Equation for the Doppler Effect
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Doppler Effect - Problem I

• A factory whistle emits a sound at 900Hz. What
  frequency will be heard by an observer in a car
  traveling at 70 km/hr
• (a) away from the source.
• (b) towards the source.
• Answer (a) 849Hz (b) 951Hz

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Doppler Effect Problem 2

• Two trains emit whistles of the same frequency,
  380Hz. If one train is at rest and the other is
  traveling at 90 km/hr away from an observer at
  rest, what will the observer detect as the beat
  frequency?
• Answer 26 Hz

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Geometrical Optics.

• Laws of reflection and refraction.
• Images from by lenses and mirrors.
• Polarization.

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The Ray Model of Light.

• The ray model of light assumes that light travels
  in straight-line paths called light rays.
• For example, a point source of light like the sun
  casts distinct shadows and the beam of a torch
  appears to be a straight line.
• Our whole orientation to the physical world is
  based on this assumption.

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Reflection of Light

• Reflectance is the ratio of the light reflected
  from a surface to the light falling on the
  surface. It is commonly expressed as a
  percentage.
• For example, the reflectance from a smooth silver
  surface is about 95 (with only small amount of
  scattering) whereas black surfaces have
  reflectances of about 5 or less.

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Laws of Reflection

• 1. The angle of incidence, i, is equal to the
  angle of reflection r.
• 2. The incident ray, the reflected ray and the
  normal to the reflecting surface all lie in the
  same plane.

Normal
Incident ray
Reflected ray
i r
Reflecting surface.
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Images formed by plane mirrors.
Object
Image - notice that it is the same distance away
from the mirror
The image is virtual, erect and the same size as
the object.
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The Speed of Light and the Index of Refraction.

• The accepted value for the speed of light, c, in
  vacuum is 2.99792458 x 108 m/s
• This is usually rounded off to 3.00 x 108 m/s.
• The speed of light in other materials (eg glass,
  air..) is less. For example, it is 3/4c in
  water.
• The ratio of the speed of light in a vacuum to
  the speed, v, in a given material is called the
  index of refraction, n, of that material.
  Therefore
• n c/v

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Indices of Refraction
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Index of Refraction.

• Since diamond has a n2.42, the speed of light in
  diamond is
• v c n 3.00 x 108 2.42 1.24 x 108 m/s
• What is the speed of light in salt solution?
• (answer 1.96 x 108 m/s)

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Refraction
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Refraction Snells Law.

• Snells Law

The incident ray, the refracted ray, and the
normal to the boundary at the point of incidence
all lie in the same plane.
When light passes from an optically less dense
medium into an optically more dense medium, the
light ray is bent towards the normal.
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Refraction and the critical angle
Medium 1

• The critical angle is that angle that results
  with the refracted ray making an angle of 90
  with the normal and travels along the boundary
  between the two media.

Critical Angle
Medium 2
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Refraction and apparent depth.
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Refraction and Dispersion
Light entering a prism is refracted towards the
normal, and the emerging ray is refracted away
from the normal, turning the ray through a
considerable angle. Because the refractive index
of a substance varies for the different
wavelengths, a prism can spread out the various
wavelengths of light contained in an incident
beam and form a spectrum.
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How are Rainbows formed?
Only one wavelength from a rain drop makes it
into the eye. But there are many rain drops, in
many different positions and because light will
interact with each rain drop in the same way,
there is steady progression from long wavelengths
(red) near the top of the rainbow to short
wavelengths (blue) near the bottom of the rainbow
with the yellow and green colors in between.
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Formation of images by spherical mirrors.
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Curved Mirrors
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Images formed by lenses
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Real Verses Virtual Images.

• A virtual image is one where the rays of light do
  not actually pass through the image, a piece of
  white paper or film placed a the image would not
  detect the image.
• A real image is one where the light does pass
  through the image and which therefore could
  appear on paper or film placed at the image
  position.

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Converging Diverging Lenses
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Mathematics of Lenses and Mirrors
Positive and Negative numbers Negative ?
Virtual Positive ? Real
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Mathematics of Lenses and Mirrors
Note that this virtual image is formed on the
same side as the object.
Note the positive value for the focal length as
it is a real focus, and the negative value for
the image distance as it is a virtual image.
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Images formed by Concave Lenses
Note that this virtual image is formed on the
same side as the object.
Note the negative value for the focal length for
a diverging lens as it is a virtual focus.
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Images formed by Concave Mirrors.
Image forms here
Note that the mathematical relationship is the
same as for lenses, except that the REAL image is
formed on the same side as the object.
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Chromatic Aberration
ChromaticAberration The non-focusing of light
due to differing wavelengths.
The solution is to introduce another lens. This
combination of lenses is known as an Achromatic
Lens
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Spherical Aberration
Spherical Aberration the non-focusing of light
due to the shape of the mirror.
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The Eye and common defects
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Eyes and Corrective measures.
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Some Optical Instruments.
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Some Optical Instruments.
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Light waves Electromagnetic Model.
Light waves are produced by vibrating electric
charges.
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Polarisation of light.

• If you could view an electromagnetic wave
  traveling towards you, then you would observe the
  vibrations of the wave occurring in more than one
  plane of vibration. This is knowed as unpolarized
  light.
• The process of transforming unpolarized light
  into polarized light is known as polarization.

More information on polarization is available
at http//www.physicsclassroom.com/Class/light/U12
L1e.html
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How does Polarization work?