Waves

A Model For Periodic Motion

Waves

A Wave...

a disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature.

Initial Definitions

• A pulse is a single vibratory disturbance which moves from point to point through a medium.
• A wave is several pulses generated at regular time intervals.

A Wave

Another Wave

BIG IDEA

Waves transfer energy without transfering mass

Wave Classifications

Wave Classifications

Water Waves

Talk and Notes

Wave Characteristics

• The frequency () is the number of waves passing a point per unit time.
  • Frequency is measured in Hertz (Hz) or 1/s (s)
• The period of a wave () is the time for one complete cycle to pass a point
  • It is the reciprocal of frequency. , where is the period in second and is the frequency in hertz.

Check Your Understanding

What is the period of a Hz electromagnetic wave traveling at m/s?

Wave Characteristics

• The wavelength (, greek lambda, "lamb-duh") is the distance between corresponding points in phase on successive waves.
  • Measured in meters.

Wave Characteristics

The amplitude of a wave is related to the energy of a wave.

• In a transverse wave it is defined as the maximum distance above, or below, the wave axis (or equilibrium position)
• In a longitudinal wave it is determined by the maximum displacement of a particle.
• As the amplitude of a light wave increases the brightness of the light increases.
• As the amplitude of a sound wave increases the loudness increases

Check your understanding

Draw the following 4 waves: A, B, C, and D

1. A has twice the amplitude of B and half the period of B.
2. B has twice the amplitude of C and C has 5 times the frequency of B.
3. D has the same period of A, but half the amplitude.
4. A should be drawn with 2 full waves

Pivot - Wave Speed Experiment

Wave Characteristics

• The velocity of a wave is determined by the medium it is traveling in
  • Example: Sound waves travel faster in water and solids than it does in air
• Wave Equation: or
• For Electromagnetic (E&M) Waves: they move at the speed of light, , in a vacuum.
  • m/s

Check your understanding

1. The sound produced by a trumpet has a frequency of 440 Hz. What is the distance between successive compressions in the sound wave as it travels through the air at STP?
2. A stationary research ship uses sonar to send a 1180 Hz sound wave down through ocean water. The reflected sound wave from the flat ocean bottom 324 meters below the ship is detected 0.425 s after it was sent from the ship
   1. Calculate the speed of the sound wave in the ocean water
   2. Calculate the wavelength of the sound wave in the water.
   3. Determine the period of the sound wave in the water.

Wave Front

• A wave front is the locus of adjacent points of a propogated wave that are in phase.

Wave Phase

• We can think of a wave cycle as 360 degrees
• If we look at the sine graph of a wave

Wave Phase

Wave Phase

Pivot - Pulse Reflections

Pivot - Pulse "Collisions"

Pulse Reflections

• Pulse at a fixed boundaary
  • The pulse is inverted (flipped), amplitude remains the same, but opposite sign.

Pulse Reflections

• Pulse at a free boundaary
  • The pulse is reflected and remains the same

Pulse Reflections

• From a low density to a high density:
  • Original pulse is reflected and inverted
  • A new pulse moves slower through the higher density medium.

Pulse Reflections

• From a high density to a low density:
  • Original wave is reflected and is not inverted
  • New pulse moves with a faster velocity through the lower density medium

Interference

• Interference is the effect produced by two or more waves which are passing simultaneously through a region.
• Superposition is the resultant disturbance at any point is the algebraic sum of displacements due to individual waves.

Interference

Constructive Interferece

• Occurs at points where path distances to the two different sources differ by an even number of half wavelengths.
  • This means a phase difference of 0º or 360º for maximum constructive interference.

Destructive Interference

• Occurs when crests meet troughs or compressions meet rarefactions.
  • This is where path differences to the two sources differ by an odd number of half wavelengths.
  • This is at 180º out of phase.

Sound Wave Interference - Monopole

Sound Wave Interference - Dipole

SWI - Lateral Quadrupole Source

Standing Waves

Standing Waves

Standing Waves - Soft Boundary

Standing Waves - Hard Boundary

Standing Waves - Sound

Standing Waves - Closed Tube

Standing Waves - Closed Tube

Standing Waves

• Standing waves are produced when two waves of the same frequency and amplitude travel in opposite directions in the same medium.
• Nodes appear to be standing still.
• Anti-nodes vibrate between the maximum amplitude above and below the axis.
• Standing waves are often produced by reflection of a wave train at a fixed boundary of a medium.
• Standing waves are the result of the interference of two waves.

Resonance Demo

Resonance

• Resonance occurs when one vibrating body sympathetically causes another body to vibrate.
• Natural frequency is a particular frequency that a body will vibrate if disturbed.
• Musical instruments can change notes by making different resonant frequencies. They do this by changing the length of the “tube” that vibrates creating standing waves of different lengths.

Doppler Effect Demo

The Doppler Effect

• The Doppler Effect is observed when the source or the observer of a wave is moving.
• When the source and observer are moving closer together the frequency of the wave is increased.
• When the source and observer are moving further apart the frequency of the wave is decreased.

Doppler Effect

Doppler Effect - Sonic Boom

Electromagnetic Spectrum

Electromagnetic Spectrum

• Light waves are electromagnetic waves!
• All E&M waves move through a vacuum at m/s
• The electromagnetic spectrum is the complete range of frequencies and wavelengths of electromagnetic waves.

Some Facts

• No sharp divisions between types of E&M waves.
• Classified by the methods that are used to generate them.
  • i.e. Radio waves are produced by charges accelerating in a wire.
• Microwaves are used in radar systems, for transmitting long distance telephone communications in space, and to cook food.
  • Microwaves that cook food produces a frequency that is the same as the natural rotational frequency of water molecules.
• Infrared waves appear as heat when absorbed by objects. This is why we use infrared lamps to keep food warm!

More Facts

• Visible light is about 1% of the E&M spectrum.
  • Produced by the rearrangement of electrons in atoms and molecules…more to come later.
  • The human eye can see from ~400 nm to ~700 nm
• Ultraviolet light causes sunburn! Ouch!
• X-rays are used as a diagnostic tool by physicians
• Gamma rays are emitted by radioactive nuclei. It is harmful to living tissue.

Waves at Boundaries

• When a wave hits a boundary three different things can occur:
  • Reflection: Waves bounce off the boundary
  • Transmission: Wave is transmitted into a new medium
  • Absorption: energy of the wave is transferred into the boundary medium

Light and Rays

• We can model incoming light waves as “rays” or lines that represent the direction that our light wave is moving.
• When light interacts with objects several times larger than its wavelength, it travels in straight lines and acts as a ray

Law of Reflection

Law of Reflection

The Normal Line

• The normal line, often referred to as the normal, is an imaginary line that is perpendicular to the surface at the point of incidence.

Specular Reflection

• Specular (regular) Reflection: reflection off of smooth surfaces such as mirrors or a calm body of water.
• Diffuse Reflection: reflection off of rough surfaces such as clothing, paper, and an asphalt roadway.

Refraction

Refraction is the bending of the path of light when it travels from one medium to another.

Refraction

• When light hits a boundary a portion of the light is reflected and a portion of the light is transmitted into the new boundary.
• In the new boundary the frequency remains the same, but the speed and wavelength change.
• In the new medium the path of light is bent.

Refraction!

Refraction & Reflection

Why does light slow down?

...its complicated

• Waves: oscillating particles & superposition
• Quantum Mechanics...

Index of Refraction

• Speed of light is dependent upon the optical density of the material that it is traveling through:
  • Does not depend on actual density of material
  • Greater optical density the slower the speed of light
• The indicator of optical density is a material's index of refraction
• • index of refraction
  • speed of light ( m/s)
  • speed of light in new medium

Index of Refraction (p. 2 ref table)

Check Yourself

What is the speed of light in glycerol?

What way does light bend?

• Light traveling from a fast to slow medium:
  • If light travels from a material with a low n to a higher n the light will bend towards the normal.
  • Example: Light traveling from air to water.
• Light traveling from a slow medium to a fast medium:
  • If a light travels from a medium with a high n to a lower n the light will bend away from the normal line.
  • Example: From Diamond to water.

Snell's Law

Snell's Law

• Snell's Law:
• Remember which can be rearranged to
• So we can write Snell's Law as:
• Which can also be written as:

Diffraction

• Diffraction is the spreading of waves into a regio behind a barrier in the wave's path

Wave Behavior Summary:

• Reflection: Waves bounce off of a new medium.
• Refraction: Waves bends in a new medium.
• Diffraction: Waves change direction of when traveling through an opening or around an obstacle.

Why is Diffraction Important?

• Newton believed that light was made of a stream of particles of called corpuscles.
  • This was the corpuscular theory of light.
• Diffraction proved that light behaved like a wave.

Young's Double Slit Experiment

• The year was 1801…
• And Thomas Young proved that light behaved as a wave.
• A two-point interference pattern always has alternating pattern of nodal and anti-nodal lines.

Young's Double Slit

Diffraction

• The amount of diffraction depends on:
  • Wavelength
  • Slit size
• The relationship for both are:
  • Larger wavelength = more diffraction
  • Smaller Slit = more diffraction