Vibrations and Waves
Chapter 14
Physics Principles and Problems
Zitzewitz, Elliot, Haase, Harper, Herzog,
Nelson, Nelson, Schuler and Zorn
McGraw Hill, 2005
Periodic Motion - motions that all
repeat in a regular cycle.
http://planetwize.com/wp-content/uploads/2008/08/guitar.jpg
http://www.dkimages.com/discover/previews/978/25020465.JPG
Simple Harmonic Motion
• During motion, object has
one point where the net
force is zero (equilibrium).
• Whenever the object if
pulled away from
equilibrium, the net force
becomes non-zero and
works to pull the object back
to equilibrium.
• The force needed to restore
equilibrium is directly
proportional to the
displacement of the object.
http://session.masteringphysics.com/problemAsset/1003614/10/168450A.
• Period (T) - time for the object to
complete one cycle of motion.
• Amplitude - maximum distance that the
object moves away from equilibrium.
http://hyperphysics.phy-astr.gsu.edu/Hbase/imgmec/sshm.gif
• Hooke’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 point. F = -kx
• Potential energy in a stretched or compressed spring is
equal to one half the product of the spring constant and the
square of the displacement. PEsp = 1/2kx2
http://hyperphysics.phy-astr.gsu.edu/HBASE/imgmec/hook.gif
Period of a Pendulum is equal to two times pi
times the square root of the length of the
pendulum divided by acceleration due to
gravity. T = 2√l/g
http://dev.physicslab.org/img/14c7c356-6f6e-49e4-a953-2396343435fb.gif
http://www.gailruby.com/simplependulum.gif
Resonance - the increase in the amplitude of a
vibrating or oscillating object due to the application
of small forces during regular intervals.
http://www.sciencenews.org/pages/sn_arc99/1_30_99/bridge.gif
http://www.worsleyschool.net/science/files/tacoma/pic3.JPG
• Pumping your legs when swinging.
• Wind causing the Tacoma Narrows bridge collapse.
Wave - a disturbance that carries energy through
matter or space (matter is not transferred).
http://moments.capturednature.com/wp-content/uploads/2007/01/water-ripples.jpg
• Transverse Wave - wave pulse (disturbance) vibrates
perpendicular to the direction of the wave’s motion.
• Longitudinal Wave - wave pulse (disturbance) vibrates
parallel to the direction of the wave’s motion.
http://www.geo.mtu.edu/UPSeis/images/S-wave_slinky.gif
http://www.geo.mtu.edu/UPSeis/images/P-wave_slinky.gif
Wave Measurements
• Speed - the speed of a wave pulse is equal to the
displacement of the wave peak divided by the amount
of time. v = ∆d / ∆t
• Amplitude - the maximum displacement of the wave
from its position of rest. For waves that have the same
speed, the rate of energy transfer is proportional to the
square of the amplitude.
• Wavelength - the shortest distance between points
where the wave pattern repeats itself.
• Period - the time (T) it takes wave to complete one
cycle (wavelength).
• Frequency - the number of complete oscillations it
makes each second.
http://www.physicsdaily.com/physics/upload/e/e9/Wave.png
• The frequency of a wave is equal to the
reciprocal of the period.
f=1/T
• The wavelength is equal to velocity
divided by the frequency.
=v/f
Wave Behavior
• Incident
wave - initial
wave that
strikes a
boundary.
• Reflected
wave returning
wave after
the collision
of the
incident
wave with a
boundary.
http://www.iop.org/activity/education/Teaching_Resources/Teaching%20Advanced%20P
hysics/Vibrations%20and%20Waves/Images%20300/img_mid_4472.gif
http://www1.union.edu/newmanj/lasers/Light%20as%20a%20Wave/outofphasewaves.gif
Principle of
Superposition
• When two waves
exist in the same
place in the medium
at the same time the
displacement of the
medium is equal to
sum of the two
individual wave
displacements.
http://2.bp.blogspot.com/_jbMoSCDL2ng/SZ
fBTrqqDOI/AAAAAAAAAC8/-tfsIEZoXE8/s400/superposition.gif
Wave Interference - the result of the
superposition of two or more waves.
• Destructive - when two waves with opposite
amplitudes meet. If these are equal amplitudes
then the point that they meet (node) does not
move.
• Constructive - when two waves with amplitudes
in the same direction meet. Produces an a point
where the largest amount of displacement
occurs (antinode).
http://cord.org/cm/leot/course01_mod07/loet01-07-06new.gif
http://www.lightandmatter.com/html_books/3vw/ch04/figs/standing-waves-on-floor.
• Standing waves are produced through the
constructive and destructive interference of
waves. Increasing the frequency of oscillations
increases the number of nodes and antinodes.
Waves in 2 Dimensions
http://www.dosits.org/science/sndmoves/img/angles1.gif
• When an incident wave strikes a barrier it will
be reflected. The angles formed between the
incident ray and the normal (draw line that is
perpendicular to the barrier) and the reflected
ray and the normal are equal.
http://www.gcsescience.com/Refraction-Water-Waves.gif
• Refraction is the change in direction of a wave at the
boundary between two different media.
• For example waves approaching shore will always
have the same frequency, however, their wavelength
and velocity decreases. This will cause a change in
direction between these two media.