Waves
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Waves. Periodic Motion. We are surrounded by oscillations – motions that repeat themselves Understanding periodic motion is essential for the study of waves, sound, alternating electric currents, light, etc. How many of you play an instrument?

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Waves

Waves


Periodic motion

Periodic Motion

We are surrounded by oscillations – motions that repeat themselves

Understanding periodic motion is essential for the study of waves, sound, alternating electric currents, light, etc.

How many of you play an instrument?

An object in periodic motion experiences restoring forces that bring it back toward an equilibrium position

Those same forces cause the object to “overshoot” the equilibrium position

Think of a block oscillating on a spring or a pendulum swinging back and forth past its equilibrium position Demonstrate


Definitions of a waves

Definitions of a Waves

  • A wave is a traveling disturbance that carries energy through space and matter without transferring mass.

    • Transverse Wave: A wave in which the disturbance occurs perpendicular to the direction of travel (Light).

    • Longitudinal Wave: A wave in which the disturbance occurs parallel to the line of travel of the wave (Sound).

    • Surface Wave: A wave that has charact-eristics of both transverse and longitudinal waves (Ocean Waves).

      Wave types


How does a wave vary in position and velocity full body demonstrate pva graphs

How does a wave vary in position and velocity? - Full body Demonstrate - PVA graphs


Types of waves

Types of Waves

  • Mechanical Waves: Require a material medium* such as air, water, steel of a spring or the fabric of a rope.

  • Electromagnetic Waves: Light and radio waves that can travel in the absence of a medium.

* Medium = the material through which the wave travels.


Wave motion

Wave Motion

The wave is another basic model used to describe the physical world (the particle is another example)

Any wave is characterized as some sort of “disturbance” that travels away from its source

In many cases, waves are result of oscillations

For example, sound waves produced by vibrating string

For now, we will concentrate on mechanical waves traveling through a material medium

For example: water, sound, seismic waves

The wave is the propagation of the disturbance: they do not carry the medium with it

Electromagnetic waves do not require a medium

All waves carry momentum and energy


Types of waves1

Types of Waves

In solids, both transverse and longitudinal waves can exist

Transverse waves result from shear disturbance

Longitudinal waves result from compressional disturbance

Only longitudinal waves propagate in fluids (they can be compressed but do not sustain shear stresses)

Transverse waves can travel along surface of liquid, though (due to gravity or surface tension)

Sound waves are longitudinal

Each small volume of air vibrates back and forth along direction of travel of the wave

Earthquakes generate both longitudinal (4–8 km/s P waves) and transverse (2–5 km/s S waves) seismic waves

Also surface waves which have both components


Transverse wave characteristics

Transverse Wave Characteristics

  • Crest: The high point of a wave.

  • Trough: The low point of a wave.

  • Amplitude: Maximum displacement from its position of equilibrium (undisturbed position).

John Wiley & Sons


Transverse wave characteristics cont

Transverse Wave Characteristics (cont.)

  • Frequency(f): The number of oscillations the wave makes in one second (Hertz = 1/seconds).

  • Wavelength(): The minimum distance at which the wave repeats the same pattern (= 1 cycle). Measured in meters.

  • Velocity (v): speed of the wave (m/s).

    v = f

  • Period (T):Time it takes for the wave to complete one cycle (seconds).

    T = 1/f


The inverse relationships v f

Position

Frequency

Wavelength

The Inverse Relationshipsv = f

  • The speed of a wave is determined by the medium in which it travels.

    • Since velocity is constant for a given medium, the frequency and wavelength must be inversely proportional.

      • As one increases, the other decreases


The inverse relationships t 1 f

Position

Frequency

Period

The Inverse RelationshipsT = 1/f

  • Similar to the inverse relationship for frequency and wavelength, a similar relationship exists for frequency and the period.


Waves at fixed boundaries

Waves at Fixed Boundaries

  • A wave incident upon a fixed boundary will have its energy reflected back in the opposite direction. Note that the wave pulse is inverted after reflecting off the boundary.

  • Example of Waves at Fixed Boundaries

Start Per 5/6 here

www.electron4.phys.utk.edu


Interference

Interference

  • Interference occurs whenever two waves occupy the same space at the same time.

    • Law of Linear Superposition:When two or more waves are present at the same time at the same place, the resultant disturbance is equal to the sum of the disturbances from the individual waves.


Constructive wave interference

Constructive Interference – Process by which two waves meet producing a net larger amplitude.

Constructive Wave Interference

www.electron4.phys.utk.edu


Destructive wave interference

Destructive Interference – Process by which two waves meet canceling out each other.

Destructive Wave Interference


Standing waves

Standing Waves

  • Standing Wave:An interference pattern resulting from two or more waves moving in opposite directions with the same frequency and amplitude such that they develop a consistent repeating pattern of constructive and destructive interference.

    • Node:The part of a standing wave where interference is destructive at all times (180o out of phase) .

    • Antinode:The part of the wave where interference is maximized constructively.

    • Standing Wave


Continuous waves

Continuous Waves

  • When a wave impacts a boundary, some of the energy is reflected, while some passes through.

  • The wave that passes through is called a transmitted wave.

  • A wave that is transmitted through a boundary will lose some of its energy.

    • Electromagnetic radiation will both slow down and have a shorter wavelength when going into a denser media.

    • Sound will increase in speed when transitioning into a denser media.

  • Speed of Light in different mediums


Continuous waves higher speed to lower speed

-v1

v2

v1

Boundary

Continuous Waves – Higher Speed to Lower Speed

  • Note the differences in wavelength and amplitude between of the wave in the two different mediums

Incident + Reflected Wave

Transmitted Wave

Displacement

Lower speed

Shorter wavelength

Higher speed

Longer wavelength

Note: This phenomena is seen with light traveling from air to water.


Waves at boundaries

Waves at Boundaries

  • Examples of Waves at Boundaries

  • Wave Types (Cutnell & Johnson)

  • Waves - Colorado.edu

  • Other Examples


Key ideas

Key Ideas

  • Waves transfer energy without transferring matter.

  • Longitudinal waves like that of sound require a medium.

  • Transverse waves such as electro-magnetic radiation do not require a medium.

  • In transverse waves, displacement is perpendicular to the direction of the wave while in longitudinal waves, the displacement is in the same direction.


Key ideas1

Key Ideas

  • Waves travel at different speeds in different mediums.

    • Light slows down when going from air to a liquid or solid.

    • Sound speeds up when going from air to a liquid or solid.

  • Waves can interfere with one another resulting in constructive or destructive interference.


Continuous waves lower speed to higher speed

Incident + Reflected Wave

Transmitted Wave

v2

-v1

v1

Displacement

Boundary

Higher speed

Longer wavelength

Lower speed

Shorter wavelength

Continuous Waves – Lower Speed to Higher Speed

  • Note the differences in wavelength and amplitude between of the wave in the two different mediums


Review of springs

Review of Springs

Classic example of periodic motion:

Spring exerts restoring force on block:

k = spring constant (a measure of spring stiffness)

“Slinky” has k = 1 N/m; auto suspensions have k= 105 N/m

Movie of vertical spring:

Elastic potential energy stored in spring:

Uel = 0 when x = 0 (spring relaxed)

Uelis > 0 always

We do not have freedom to pick where x = 0

Uel conserves mechanical energy

(Hooke’s Law)


Shock absorbers

Shock Absorbers

Shock absorbers provide a damping of the oscillations

A piston moves through a viscous fluid like oil

The piston has holes in it, which creates a (reduced) viscous force on the piston, regardless of the direction it moves (up or down)

Viscous force reduces amplitude of oscillations smoothly after car hits bump in road

When oil leaks out of the shock absorber, the damping is insufficient to prevent oscillations

Shock absorber is example of an underdamped oscillator (see also critically damped and overdamped)


Properties of waves

Properties of Waves

Superposition principle: The overlap of 2 or more waves (having small amplitude) results in a wave that is a point-by-point summation of each individual wave

(constructive interference)

(destructive interference)


Properties of waves1

Properties of Waves

Traveling waves can both reflect and transmit across a boundary between 2 media

Reflected wave pulse is inverted (not inverted) if wave reaches a boundary that is fixed (free to move)


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