An Introduction to Waves

Waves are everywhere. Whether we recognize or not, we encounter waves on a daily basis. Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine waves, telephone chord waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of our daily encounters with waves. 
In addition to waves, there are a variety of phenomenon in our physical world which resemble waves so closely that we can describe such phenomenon as being wave-like.   The motion of a pendulum, the motion of a mass suspended by a spring, the motion of a child on a swing, and the "Hello, Good Morning!" wave of the hand can be thought of as wave-like phenomena. Waves (and wave-like phenomena) are everywhere!

defn Vibration:  Back and forth movement over ________ .
(Diag)

defn Wave: Vibration moving through _______________ .
(Diag)

defn Energy:  Ability to change the motion of an object to:

Key Concept:  Waves transfer energy without transfer of _______________ .

defn Pulse: Single vibratory disturbance
(Diag.)

defn Periodic wave: Series of evenly timed disturbances
(Diag)

Two Types of Wave Motion:
 
Transverse:
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.		 Longitudinal:
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defn Transverse wave:  Particle motion _______________ to direction of travel of wave

Example of Transverse waves:

defn Longitudinal wave:  Particle motion  _______________ to direction of travel of wave.

 This is an example of a longitudinal mechanical wave:

Sound waves are also longitudinal waves

Click here for a simulation of transverse and longitudinal waves.(Java)
 

Characteristics of Periodic Waves

defn Frequency:  Number of waves in ____  ___________ .  formula:
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defn Period:  Number of seconds for  ____  _________ .  formulas:
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Example:  An observer standing near an inlet notices that 12 waves pass by her position in one minute.  What is the frequency of the waves? [3-steps]
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defn Amplitude:  Displacement (+,-) from equilibrium (rest) position
defn Phase:  Points having same __________ and __________ of motion.
List three pairs of points which are in phase:

1. __________  2. __________  3. ___________

defn Wavelength:  Distance between two consecutive points in phase
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defn Speed of a wave

v = ________  where v = velocity, f = frequency and l is _______________
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Periodic Wave Phenomena

defn Interference:  effect produced when two waves _______________

defn Superposition Principle:  to find the result of two overlapping waves, add their _______________ at each point
(Worksheet)
 
defn _______________ interference:  two (or more) waves add to make a __________ wave Example:
defn _______________ interference:  two (or more) waves cancel to make a __________ wave Example:

defn _______________ Waves:
The green and blue waves interfere to produce a standing wave.  (Note that only the first half of the standing wave is shown, then the animation repeats.)
This is what the resultant standing wave look like.  The nodes are points of minimum amplitude, the antinodes are points of maximum amplidude.

defn Nodes:  Points of NO__________.  Stationary.  Caused by _______________ interference.
defn Anti-Nodes:  Opposite of __________.  Points of maximum movement.  Caused by _______________ interference.

Example:  Sketch a standing wave on a guitar string.  The distance between the ends of the string is 0.80 meters and the wave consists of 5 nodes and 4 anti-nodes.  What is the wavelength of the wave?  If the speed of waves on a steel string is 1440 m/s, what is the frequency of the wave?
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Click here for a simulation of standing waves.(Java)

defn _______________ Frequency:  frequency at which an elastic object vibrates when struck
Ex:  bell, tuning fork, swing
 
Pumping a swing in rhythm with its natural frequency produces larger amplitudes
A small bell has a higher natural frequency than a large bell
defn ____________  __________________:  When an object is forced to vibrate, e.g. pluck a guitar string, strike a bell.
defn Resonance:  large increase in ______________ of vibration when a system is forced to vibrate at its _______________ frequency

Ex: Tacoma narrows bridge, opera singer shatters glass

defn Wave Front:  Shows only the ____________ of a wave
defn Ray:  Rays are _______________ to the wave fronts.  Show the ____________ of the wave.
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Sketch a transverse wave.
Under the T-wave diag show
the associated wave fronts.
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For the transverse wave shown above, the wave fronts are the short vertical line segments and the rays are the arrows pointing to the right.

Example:  Sketch the wave fronts and rays
for the waves produced when a stone is
dropped in a pond:
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defn Refraction:  __________ of a wave as it passes ____________ (not 90o) from one medium into another.

Key Concept:  waves refract because one part of the wave front changes __________ before the other.

Example:

Note:

Click here for a simulation of refraction (Java)
(WKS)

defn Diffraction:  ____________ of a wave into the region behind an obstacle

key concept: the degree of diffraction that the waves undergo depends upon the ratio of their ____________ to the ____________ of the opening through which they pass.  If the wavelength is ___________ than or __________ to the size of the opening, the wave will diffract a large amount.  If the wavelength is ____________ than the opening, the wave will diffract very ____________.

(2 Diag, l >= w, l < w)
(Demo w/SS diff cards)
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The Nature and Properties of Sound

Sound:
The above diagram shows how longitudinal waves (in this case sound) are transferred by alternating compressions and expansions (rarefactions) of the molecules of air through which they pass.

Example:  Sound wave in air with a frequency of 256 Hz at 22oC.

  1. Calculate the wavelength of the sound wave.
  2. Will this sound diffract through the classroom door?  Explain.
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defn Doppler Effect: the variation in observed frequency when there is relative motion between source and observer.

Doppler Effect Simulation (Java applet)


Ex: no v of source, fo=100 Hz

Ex: v to the right, fo=100 Hz

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The Nature and Properties of Light

defn Normal Line: a line _______________ to a surface

Newton's Particle Theory

Light consists of tiny ____________ of matter ejected from luminous bodies.

Huygens' Wave Theory

Light consists of a series of ____________ that radiate from a source.

Experiments which gave strong evidence that light is a wave:

Since light was now thought to be a wave, the question arose as to what type of wave it is, transverse or longitudinal?

defn Polarization:  The separation of waves so that the vibrations of the wave are all in the same __________.  ____________ waves can be polarized, ____________ waves cannot.
 

Experimental Summary for Light:

1.  Interference
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     Shows us that ...
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2.  Polarization
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     Shows us that ...
 
Demonstration of polarization, students find examples of polarization of light, lcd example

The Electromagnetic Spectrum

The electromagnetic spectrum contains radio waves, infrared waves, visible light waves, ultraviolet waves, x-ray waves, and gamma ray waves.
 
List a fact or two about each type of electromagnetic radiation
  • Gamma:
  • X-Rays:
  • Ultraviolet:
  • Visible:
  • Infrared:
  • Microwaves:
  • Radio
Click here for E/M wave facts

Law of Reflection

defn Law of Reflection:
When light is reflected off any surface, the angle of incidence _____ is always equal to the angle of reflection _____ as measured with respect to a normal.

defn ____________ Reflection:  Reflection produced by a ____________ surface, usually producing an image of the source.  Also called specular reflection.
defn ____________ Reflection:  The scattering of light caused by reflection from ____________ surfaces.

Images

defn Images:  An image is formed where light rays originating from the same point intersect on a surface (or appear to intersect for an observer).

Two types of Images:

  1. ____________ Image
    1. formed when light rays from a common point pass through, or are reflected by, an optical system which causes them to ____________ and intersect at a point.
  2. ____________ Image
    1. formed when light rays from a common point pass through, or are reflected by, an optical system which causes them to ____________ and appear to come from a single point.
Ex: Virtual image - the object is located on the left of the mirror, the image on the right.
List the 5 properties of virtual images:

Formation of Images by Plane (flat) Mirrors

Ex: Using ray diagrams and the law of reflection to model plane mirrors.
(See separate sheet)

(plane_mirror_ray_diagrams_wks.doc)

 Refraction of Light

  1. Effect of the medium
    1. The __________ of light waves depends on the properties of the medium
  2. Speed and refraction
    1. When a wave enters a new medium obliquely, and there is a __________ in speed, the wave bends toward the __________ (makes a smaller angle).
    2. When a wave enters a new medium obliquely, and there is a __________ in speed, the wave bends away from the __________ (makes a larger angle).
Example:

defn Absolute index of refraction:  the ratio of the speed of light in a vacuum to the speed of light in the medium.
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n =
where: Questions: defn Snell's Law:  The ratio of the absolute indices of refraction is inversely proportional to the ratio of the sine of the incident angle to the sine of the refractive angle.  The diagram below shows light refracting in water.  Note that q1 is the angle of incidence; it is the angle w.r.t. the normal in the medium where the light originates.  q2  is the angle of refraction.  It is also measured w.r.t the normal.

 Question:  Based on the diagram and the definition above, write a mathematical statement of Snell's Law.
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Note:  Snell's law can only be applied to a single interface ...
(diag)
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Example:  Light enters a square block of crown glass from water at an angle of 47o w.r.t. the normal.  Diagram:

The General Interface Relationship

Snell's law is a mathematical model which allows us to work with the relationships between the angles light rays make when they refract and the different speeds of light in various media. (The speeds are expressed as absolute indicies of refraction.)

When light enters a new medium and refracts, its ____________ changes.  So does the ____________ and ____________ of the light.  The general interface relationship will allow us to put all of these concepts together in one mathematical model.

We start with the following relationships and definitions:

  1. Snell's Law:
  2. definition of the absolute index of refraction:
  3. wave equation:
and we can show:
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Finally, the General Interface Relationship is:
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When solving problems with the G.I.R. remember:  Parts is Parts!

Example: Light enters a square block of flint glass from air.

  1. If the frequency of light is 7.0E14 Hz in air, what is the frequency of the light in flint glass?
  2. What is the wavelength of this light in air? (Hint: since n of air is 1.00 the speed of light in air is c.)
  3. What is the color of the light in air?
  4. What is the wavelenth of the light in flint glass?
  5. Using the wavelength information, calculate the speed of light in flint glass.
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Dispersion

defn Polychromatic Light: Light composed of different ____________.  (different wavelengths, different colors)
defn Dispersive Medium: A substance in which the ____________ of a wave depends on its wavelength.
defn ____________________: Separation of polychromatic light into its component wavelengths as the light enters a dispersive medium.  Each wavelength of light bends a slightly different amount so the wavelengths (colors) become separated.  REMEMBER:  ____________  ____________  ____________ .

Sketch the following in the space provided below:

  1. Ray diagram of monochromatic light passing through a triangular prism.  Sketch a normal at each interface and show the direction of the refracted light ray.
  2. Ray diagram of polychromatic light passing through a triangular prism.  Show dispersion starting at the first interface and continuing as light exits the prism.
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defn Non-dispersive Medium: A substance in which the speed of the wave does not depend on its ____________.  A vacuum is a non-dispersive medium for light.  Under everyday classroom conditions, air is a non-dispersive medium for light as well.

Left: Rainbows are produced by a combination of total internal reflection and ____________________.
Right: The light from many raindrops combines to form the (virtual image) rainbow that we see.
 

Interference of Light

Review:  The demonstration of light interference in 1802 by ____________  ____________ is a classic physics experiment.  Young's experiment gave strong evidence that light is a wave.  ____________ implies that light is a transverse wave.  James Clerk ____________ concluded that light waves were made of two of the fundamental forces of nature, electricity and magnetism. (Video)

defn ____________ Light:  Light produced by sources which maintain a constant ____________ relationship.

Sketch a diagram of coherent light waves:

Young was sucessful where others had failed because he figured out a way to make coherent light that he could use in his interference experiment.  Without coherent light the constructive and destructive interference of light will be random at any point in space and all evidence of interference will be lost.  Using coherent light provides an interference pattern which persists over time and can be studied.

Sketch a diagram of the apparatus used in Young's interference experiment.
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