Vibrations and Waves Waves 2011-2012. Periodic Motion Periodic motion – a motion that repeats in a regular cycle. Simple harmonic motion – results when.

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.