Summary Sheet – Waves, Sound, Electricity, Magnetism, Light
A. A particle will oscillate if it is given some initial energy and is acted upon by a restoring
force. A restoring force is a force that changes direction and magnitude in such a way as to
always push the particle back to a central equilibrium position. At the equilibrium position
the restoring force is zero.
B. When an oscillating particle has returned to its initial position and initial velocity, it has
completed one cycle. The period of oscillation is the time to complete one cycle. The
frequency of oscillation is the number of cycles completed per second. Two common
oscillating systems are a mass on a spring and a pendulum, and their periods are:
Tspring
m
= 2π
k
m = mass
k = spring force constant
Tpendulum
L
= 2π
g
L = pendulum length
g = acc. gravity
C. Resonance occurs when a periodic force is applied to an oscillator with a frequency that
matches the natural frequency of the oscillator. A large increase in the amplitude of
oscillation results.
D. Waves transport energy, not material. Waves can be classified as nonrecurrent, periodic,
transverse, or longitudinal.
E. The speed of a wave is determined by the properties of the medium that the wave is traveling
through. The wavelength is the distance between two crests or two troughs of a wave. The
frequency is the number of crests or troughs that pass by a point in space each second. The
frequency times the wavelength is equal to the speed of propagation of the wave. f λ = v
where f is the frequency, λ is the wavelength, and v is the speed.
F. Waves behave differently than particles.
1) Reflection - when waves reflect from a barrier they are inverted, but particles are not.
2) Interference - when waves meet they pass through each other, but particles collide
with each other. When waves overlap the resulting amplitude is the sum of the
individual wave amplitudes. When a crest overlaps a crest there is constructive
interference and when a crest overlaps a trough there is destructive interference.
3) Diffraction - waves bend when passing through barriers, but particles continue
straight ahead. The angle of diffraction bending depends upon the wavelength and
the size of the opening or barrier.
G. Standing waves occur when a wave hits a barrier, reflects back, and interferes with itself.
Places of constructive interference are called antinodes and places of destructive interference
(zero amplitude) are called nodes.
H. Sound is a longitudinal wave that is caused by periodic compression of the molecules in the
medium. Musical instruments create sound by causing standing waves to occur. Each
musical instrument is distinguishable by the harmonics of the standing waves it creates.
I. Electric charges come in two varieties we call positive and negative. A neutral object has
equal numbers of positive and negative charges, a charged object has more of one kind than
the other. Charges flow freely through conductors but not through insulators.
J. Like charges repel; unlike charges attract. A charged object can attract a neutral object by
inducing a separation of charge in the neutral object. The electric force, called Coulomb’s
Law, has a mathematical form similar to the gravitational force.
Felectrical = k
q1 q2
d2
where k = 9.0 × 10 9 N⋅ m 2 C 2 and q1, q2 are the charges separated by distance d.
K. Electric charges are surrounded by an electric field equal to the force experienced by a unit
positive charge (+1.0 C). E = Felectrical / q. The electrical potential energy of a charged object
in an electric field is equal to the work done in bringing the charged object from some zero
reference location. It’s also the energy the object would gain if any constraints are removed.
The electric potential is the potential energy per charge, measured in Volts (V) = J / C.
L. When there is a complete pathway and a voltage difference through the pathway, electric
current flows, measured in Amperes (A) = C / s. The characteristics of the circuit can be
determined by Ohm’s law, V = I R. The resistance R is measured in Ohms, 1 Ω = 1.0 V / A.
The power in an electrical circuit is equal to P = I V and is measured in Watts (W).
M. Magnets have two poles that behave like charges; like poles repel and unlike poles attract.
However, magnetic poles always occur in pairs. Magnets attract some materials like iron,
but have no effect on other materials. The Earth is a giant magnet.
N. Electrical currents produce magnetic fields, and in fact all magnetic fields originate from
electrical currents, even in permanent magnets.
O. Steady magnetic fields exert forces on electrical currents but not on stationary charges.
P. If a magnet and a loop of wire move relative to each other in such a way that the magnetic
field through a loop is either increased or decreased, a current is produced in the wire
(Faraday’s law). The current flows in a direction such that it produces a magnetic field that
opposes the change in the magnetic field through the loop (Lenz’s law). The voltage (and
hence the current) generated in the loop depends on the rate of change of the magnetic field the faster the change, the larger the voltage. Likewise, changing the current in the loop
changes the magnetic field through the loop. These principles describe the physics of
voltage transformers, generators, and motors.
Q. Anytime a charge is accelerated, an electromagnetic wave is generated that can travel
through empty space. The accelerating charge causes a changing electric field, which in turn
produces a changing magnetic field, and so on. Electromagnetic waves are a combination of
oscillating electric and magnetic fields. Light, radio, TV, and X-ray waves are all examples
of electromagnetic waves.
R. Light travels in straight lines, and is only visible if it enters our eyes. Shadows consist of an
umbra and a penumbra. Light travels at c = 299,792,458 m/s ≈ 3×108 m/s.
S. The law of reflection is defined in terms of the normal to the
reflecting surface.
Law of reflection: θi = θr
reflected ray
θr
θi
normal
T. Mirrors can produce both real and virtual images. A plane mirror produces a virtual image
of the object, and the image is as far behind the mirror as the object is in front of the mirror.
U. Our perception of color can be described in terms of three primary colors, red, green, and
blue, and their complements, cyan, magenta, and yellow, respectively. Color is determined
by the wavelength of light, with red light having a longer wavelength than blue light.
V. Light is a wave. The speed of propagation of a wave is determined only by the medium it
travels through, and the index of refraction (n) is used to describe the speed of a light wave
through a medium.
n=
c
the ratio of speed of light in a vacuum to the speed of light in a material.
v
W. The fact that the speed of light is different in a medium causes light to bend when it enters
the medium, a process called refraction. Snell’s law describes refraction: if the light goes
from medium 1 into medium 2, n 1 sin θ 1 = n 2 sin θ 2 , where θ1 is the incident angle and θ2
is the transmitted angle, both measured relative to the normal. The law of refraction applies
to lenses, but the image in a lens can be found easiest by using three special rays: (i) parallel
to the optic axis (OA), goes through the principal focal point (FP); (ii) through other focal
point FO, goes parallel to OA; (iii) through the center of the lens, goes straight through (not
bent).
X. Light exhibits interference and diffraction, both of which are characteristics of waves but not
particles. Thin films can produce interference patterns, where bright reflections correspond
to a minimum film thickness of λf / 4, where λf = λvacuum / n. That is, the wavelength in the
film is shorter than the wavelength in vacuum by a factor of n. Diffraction patterns are
produced when light passes through a narrow opening. The narrower the opening, the wider
the diffraction pattern.