Chapter 11 - Oscillators and Waves

Mathematical Representation

Where θ is the angular spread of a wave, and l is the width of the opening or object it passes around 11.15 ________ of a Travelling Wave • Expressing a sinusoidal wave mathematically, th follwoing equation is used 2π y= A sin x λ Where y is the displacement, A is the desired amplitude, λ is wavelength, and x is simply the x axis • Waves move, and the distance after moving over a specified amount of time is given by vt, inserting this into the previous equation gives.

FT

Where ________ is the force of tension within the string and µ is the mass by length (µ= m /l) of the cord Speed of Longitudinal Waves • The speed of a longitudinal wave travelling down a solid rod is.

SHM

Where x starts at 0 instead of A • Sinusoidal- Having the shape of a sine function, simple harmonic motion is sinusoidal Velocity and Acceleration as a Function of Time • Graphing velocity in ________ as a function of time gives.

Periodic

Describe motion of objects that move back and forth

Equilibrium position

The position of an oscillator where it exerts no force, such as a spring that remains still

Simple Harmonic Motion (SHM)

Describes a system where restoring force is proportional to the negative of the displacement

Amplitude

The greatest distance from the equilibrium point of a simple harmonic oscillator, represented by A

Simple Pendulum

A small object on a cord that does not stretch and has negligible mass

Damped Harmonic Motion

Harmonic motion whose amplitude decreases as number of swings increases, such as by friction

Underdamped

Describes a damped system that oscillates multiples times before stopping

Overdamped

Describes a damped sysem that does not oscillated at all before stopping

Critical Damping

Damping that causes motion to stop in the shortest amount of time

Shock Absorbers

An example of a critically damped system, but as they wear out, underdamping occurs

Forces Oscillation

A situation where which an object is forced to oscillate at a frequency other than it's natural frequency

Natural Frequency

Also called resonant frequency, this is the frequency at which an a springoscillates when no force is applied to it during oscillation

Resonance

Occurs when forced frequency and natural frequency are equal and act at the same time

Mechanical Waves

Oscillations of matter

Pulse

A single bump in a wave

Transverse Wave

A wave whose particles move perpendicular to the waves, such as an ocean wavewhere the water moves vertically but the wave travels horizontally

Longitudinal Wave

A wave whose particles move parallel to the direction of the wave, such as asound wave moving horizontally, its particles will also oscillate horizontally

Medium

The material or space through which a wave travels

Wave Front

All the points along the wave that form its crest

Ray

A line in the direction of wave motion, perpendicular to its front

Plane Waves

Wave fronts that have lost their curvature and are straight

Law of Reflection

The angle of reflection equals the angel of incidence

Angle of Incidence

The angle between the direction of a wave and the perpendicular of the surface it reflects off of

Angle of Reflection

The angle of incidence reflected across the perpendicular to the surface of reflection

Interference

Occurs when two waves pass through the same region of space

Principle of Superposition

The resultant displacement is the algebraic sum of their separate displacements

Destructive Interference

Occurs when waves have opposite displacements and cancel out

Constructive Interference

Occurs when waves have equal displacements and combine

Phase

Used to describe the relative position of the crests of two waves

Node

Point at which a standing wave is still

Antinode

Point at which a cord oscillates with maximum amplitude

Natural Frequency

A frequency at which a cord forms a standing wave

Fundamental Frequency

Lowest natural frequency of a wave, one antinode

Overtones

Other natural freuqncies, these are multiples of the fundamental, also called harmonics

Refraction

Occurs when a wave crosses into a new medium, its speed and direction change

Diffraction

The bending of a wave when it encounters an obstacle