waves, optics, and modern physics unit 1

terms and definitions from unit 1

periodic motion

any motion that repeats itself at regular time intervals

period

time to complete one oscillation

frequency

number of events per unit time

oscillation

one complete cycle of periodic motion

simple harmonic motion (SHM)

motion in which the acceleration (and therefore net force) of the system is proportional to the displacement and acts in the opposite direction of the displacement

amplitude

maximum distance of an object from its equilibrium position in SHM

force constant (k)

representation of the stiffness of an object

equilibrium position

rest position for an object in SHM where net force is zero

phase shift

shift of a sine or cosine function left or right along the x-axis

stable equilibrium point

when the forces on both sides of the equilibrium position point towards the equilibrium position, if an object at equilibrium is disturbed, it will return to its equilibrium position

unstable equilibrium point

when the forces on either or both of the sides of the equilibrium position point away from the equilibrium position, if an object at equilibrium is disturbed, it will not return to its equilibrium position

simple pendulum

a point mass (also called a pendulum bob) which is suspended from a string with negligible mass

physical pendulum

any object whose oscillations are similar to those of a simple pendulum, but cannot be modeled as a point mass on a strong

torsional pendulum

a rigid body suspended by a light wire or spring which when twisted oscillates between two maximum angular displacements

natural angular frequency

angular frequency of a mass undergoing SHM

underdamped system

system with a small damping constant (smaller than √4mk), where the amplitude of the motion decays exponentially

critically damped system

system with a damping constant equal to √4mk, where the system asymptotically approaches the equilibrium as quickly as possible without oscillation

overdamped system

system with a large damping constant (larger than √4mk), where the system will approach equilibrium over a longer period of time without oscillation

natural frequency

the frequency at which a system would oscillate if there were no driving and no damping force

resonance

the phenomenon of driving a system with a frequency equal to its natural frequency

transients

the motions of the oscillator forced with a periodic driving force

quality of a system

spread of the angular frequency at half the maximum amplitude divided by the natural frequency

constructive interference

when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs

destructive interference

when two identical waves arrive at the same point exactly out of phase; that is, precisely aligned crest to trough

fixed boundary condition

when the medium at a boundary is fixed in place so it cannot move

free boundary condition

exists when the medium at the boundary is free to move (not fixed)

intensity

power per unit area

interference

overlap of two or more waves at the same point and time

linear wave equation

equation describing waves that result from a linear restoring force of the medium

longitudinal wave

wave in which the disturbance is parallel to the direction of propagation

mechanical wave

wave that is governed by Newton’s laws and requires a medium

pulse

single disturbance that moves through a medium, transferring energy but not mass

superposition

phenomenon that occurs when two or more waves arrive at the same point

transverse wave

wave in which the disturbance is perpendicular to the direction of propagation

wave

disturbance that moves from its source and carries energy

wave function

mathematical model of the position of particles of the medium

wave number

equal to the ratio of the angle and the position of a periodic function

wave velocity / propagation velocity

velocity at which the disturbance moves

wavelength

distance between adjacent identical parts of a wave

standing wave

wave that, under certain conditions, can bounce back and forth through a particular region, effectively becoming stationary

node

x-positions of a standing wave that are always zero

antinode

x-positions of a standing wave that are alternate between the positive and negative amplitudes

fundamental frequency

frequency driving the first (fundamental, first harmonic) node, the lowest frequency that will produce a standing wave

overtone

all frequencies above the fundamental frequency which produce a standing wave

normal mode

possible standing wave pattern for a string, with normal frequencies

harmonic

resonant frequency that is an integral multiple of the fundamental