Chapter 15 - Waves Traveling Waves –Types –Classification –Harmonic Waves –Definitions –Direction of Travel Speed of Waves Energy of a Wave Standing Waves.

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Presentation transcript:

Chapter 15 - Waves Traveling Waves –Types –Classification –Harmonic Waves –Definitions –Direction of Travel Speed of Waves Energy of a Wave Standing Waves –Reflection and Transmission –Superposition and Interference (Refraction and Refraction)

Types of Waves Mechanical Waves - Those waves resulting from the physical displacement of part of the medium from equilibrium. Electromagnetic Waves - Those wave resulting from the exchange of energy between an electric and magnetic field. Matter Waves - Those associated with the wave-like properties of elementary particles.

Requirements for Mechanical Waves Some sort of disturbance A Medium that can be disturbed Physical connection or mechanism through which adjacent portions of the medium can influence each other.

Classification of Waves Transverse Waves - The particles of the medium undergo displacements in a direction perpendicular to the wave velocity –Polarization - The orientation of the displacement of a transverse wave. Longitudinal (Compression) Waves - The particles of the medium undergo displacements in a direction parallel to the direction of wave motion. –Condensation/Rarefraction

Waves on the surface of a liquid

3D Waves

Sound Waves

Harmonic Waves Transverse displacement looks like: A

Let the wave move vt

Standing at the origin Transverse displacement looks like:  DmDm

Phase Velocity Wave velocity is a function of the properties of the medium transporting the wave

That negative sign Wave moving right Wave moving left

Alternate notation Wave number Angular frequency

Definitions Amplitude - (A, y m ) Maximum value of the displacement of a particle in a medium (radius of circular motion). Wavelength - ( ) The spatial distance between any two points that behave identically, i.e. have the same amplitude, move in the same direction (spatial period) Wave Number - (k) Amount the phase changes per unit length of wave travel. (spatial frequency, angular wavenumber) Period - (T) Time for a particle/system to complete one cycle. Frequency - (f) The number of cycles or oscillations completed in a period of time Angular Frequency -  Time rate of change of the phase. Phase -  kx -  t  Time varying argument of the trigonometric function. Phase Velocity - (v) The velocity at which the disturbance is moving through the medium

Velocity of transverse wave in a cord

General rule for wave speeds Longitudinal wave in a long bar Longitudinal wave in a fluid

Superposition Waves in the same medium will add displacement when at the same position in the medium at the same time. Overlapping waves do not in any way alter the travel of each other (only the medium is effected)

Superposition in reverse Fourier’s Theorem – any complex wave can be constructed from a sum of pure sinusoidal waves of different amplitudes and frequencies

Interference (Superposition of equal amplitude waves) Constructive Destructive

Interference of harmonic waves Constructive - Waves are in phase. Amplitude doubling occurs Destructive - Waves are 180 degrees out of phase. Amplitude cancellation occurs

Reflection Fixed Boundary “Flips” Free Boundary Doesn’t flip”

Standing Waves - Resonance

Nodes and Antinodes Node – position of no displacement Antinode – position of maximum displacement

Natural frequencies

Energy in a Wave

Intensity

Two dimensional wave reflection