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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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
* Medium = the material through which the wave travels.
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
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
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v = f
T = 1/f
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Constructive Interference – Process by which two waves meet producing a net larger amplitude.
Destructive Interference – Process by which two waves meet canceling out each other.
Incident + Reflected Wave
Note: This phenomena is seen with light traveling from air to water.
Incident + Reflected Wave
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
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)
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
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)