Chapter 12- Vibrations and Waves

Drum_vibration_mode21.gif
vibration of a circular eardrum
Image from: http://en.wikipedia.org/wiki/Vibration
12-1
Any periodic motion is a mass attached to a spring
At equilibrium, velocity reaches a max while spring force and acceleration are zero
at maximum displacement (opposite of equilibrium), spring force and acceleration reach a max
Restoring force: pushes or pulls mass back toward equilibrium

HOOKE'S LAW:
For a given spring the force the spring exerts is proportional to the negative of the distance that the spring is stretched from rest.

Simple Harmonic Motion: the repetitive, back-and-forth motion of an object. ex: pendulum or a mass oscillating on the end of a spring
-When graphed, the displacement (x), velocity (v), and acceleration (a) of an object in simple harmonic motion in respect to time are all sinusoids:
-In simple harmonic motion, restoring force and acceleration are maximum at maximum displacement and velocity is maximum at equilibrium.
-For all small angles of displacement (<15 degrees), a pendulum swings with simple harmonic motion.
-A stretched or compressed spring has elastic potential energy
-Gravitational potential increases as a pendulum's displacement increases

21:2:
Wave.png
http://en.wikipedia.org/wiki/Wave

Wave: a motion of disturbance
medium: material through which a disturbance travels
-all waves need a medium to travel through
-soundwaves can't travel through space, because it's a vaccuum
Amplitude: how far the object moves
Period: time it takes for one complete cycle of motion
Frequency: the number of complete cycles of motion occuring in one second


Period a pendulum when given length:

Period of a spring when given mass:


12:3:

-A wave is a motion of disturbance
-Medium: the material through which a disturbance travels
-all waves need a medium to travel through
-sound waves can’t travel through space because it is a vacuum (no medium)
- Mechanical wave: a wave that propagates through a deformable, elastic medium

-Transverse Wave: the vibrations of the wave are perpendicular to the direction of motion of the wave
-Longitudinal Wave: the vibrations of the wave are parallel to the direction of motion of the wave
-Wavelength: the shortest distance between corresponding parts of two waves
-Crest: highest point on a wave
-Trough: lowest point on a wave
Wavelength: the distance between two adjacent points of the wave, such as a crest to a crest

-Wave speed: the speed with which a wave propagates




12.4:
-When two or more waves come together they pass through each other, and through the principle of superposition the total displacement of the medium is equal to the sum of the displacements of the overlapping waves at each point.
-Constructive interference: when two waves overlap with displacements in the same direction the resulting wave has an amplitude greater than either of the two overlapping waves
-Destructive interference: when two overlapping waves have displacements in opposite directions the resulting wave will have a displacement less than the displacement less than the displacement of the wave with larger amplitude, possibly even no displacement at all.
-A wave will invert when it travels through some medium and reaches a fixed boundary; the wave will reflect back inverted with respect to the initial wave.
-If the wave reflects off of a free boundary, the wave will reflect off the boundary in the same orientation that it arrived.
-Standing Wave: when a wave is traveling in a confined space with just the right frequency. it ressults from a wave constructively and destructively interfering with its own reflection.
-Ends of standing wave:
-nodes (where complete destructive interference occurs)
-Anti-node: where constructive interference causes oscillation to reach a relative max amplitude
nodes_and_antinodes.gif
Fundamental nodes and antinodes

Image from http://hyperphysics.phy-astr.gsu.edu/hbase/waves/imgwav/ohar.gif

Node
Length
Lambda
Simplified
1



2



3



4




"Chapter 12: Vibrations and Waves." Holt Online Learning. 5 June 2009 <my.hrw.com/tabnav/controller.jsp?isbn=0030724864>.