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Vibrations and WavesWaves2011-2012
Periodic MotionPeriodic motion – a motion that
repeats in a regular cycle.
Simple harmonic motion – results when the restoring force on an object is directly proportional to the object’s displacement from equilibrium
Periodic MotionPeriod – T – time needed for an
object to repeat one complete cycle
Amplitude – the maximum distance that the object moves from equilibrium
Mass on a SpringHooke’s Law:
◦The force exerted by a spring is equal to the spring constant times the distance the spring is compressed or stretched from its equilibrium position.
◦k is the spring constant, which is related to the stiffness of the spring.
Mass on a SpringPotential Energy
◦When a spring is stretched or compressed, there is some amount of potential energy (the spring wants to return to its equilibrium position).
◦The potential energy in a spring is equal to one-half times the product of the spring constant and the square of the displacement.
PendulumsA pendulum consists of a
massive object, bob, suspended by a string or rod of length l.
Period of a pendulum:
ResonanceOccurs when small forces are applied
at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases.
Special form of SHM in which the additions of small amounts of force at specific times in the motion of an object cause a larger and larger displacement.
Parts of a Sine Wave
crests – the high points of a wave
troughs – the low points of a wave
amplitude – the distance between the equilibrium point and the top of a crest (or bottom of a trough)
wavelength – the distance between identical points on a wave
Parts of a Sine Wave
wavelength
amplitude
crest
trough
Calculating Frequency and Period
fT
1
Tf
1
Frequency Period
Wave Speed
The speed of a wave depends on the medium through which the wave moves.
The speed, wavelength, and frequency are related.
fv
Transverse Waves
Whenever the motion of the medium is at right angles to the direction in which a wave travels
Longitudinal Waves
The particles move along the direction of the wave rather than at right angles to it.
Interference
Interference pattern – waves that are in the same plane can overlap and interfere with one another
Constructive interference – when the crest of one wave overlaps the crest of another, their individual effects add together
Destructive interference – when the crest of one wave overlaps the trough of another, their individual effects are reduced
+ =
+ =
Constructive Interference
Destructive Interference
Standing Waves
Standing wave – Suppose a rope is attached to a wall. You shake the rope up and down and cause a sine wave. This is a standing wave.
Node – point on the rope where there is no change in amplitude
Antinode – points on the rope where there is maximum amplitude
Reflected Waves
When a wave encounters a boundary, it will reflect back.
The way in which it reflects will vary depending on whether it encounters a fixed or free boundary.
Fixed Boundary
A fixed boundary is when a wave encounters a fixed surface. This would occur for a rope attached to a wall.
Reflection at a Fixed Boundary
Incident wave
Reflected wave
Free Boundary
A free boundary occurs when, for example, a rope is attached to a post and is free to move up and down at the end.
Reflection at a Free Boundary
Incident wave
Reflected wave
Less Dense More Dense
Incident Pulse
Reflected Pulse Transmitted Pulse
More Dense Less Dense
Incident Pulse
Reflected Pulse Transmitted Pulse
Reflection and RefractionReflection
◦Waves bounce back off of a surface that they encounter.
Refraction◦Waves bend and pass through a
surface that they encounter.