
Where do we encounter waves? Write down
all the examples of waves that you can think
of.
Chapter 14


A periodic motion repeats in a regular cycle.
Examples include:
◦ Pendulums (such as on a grandfather clock)
◦ A mass at the end of a spring
◦ Vibrating guitar string


The period is the amount of time for one
complete cycle.
The amplitude is the maximum amount that
the object moves from its equilibrium
position
x


When you stretch or compress a spring, the
spring exerts a force to return it to its
equilibrium position.
The amount of force is given by Hooke’s Law
Fsp  kx


where 𝑘 is the spring constant (a property of
the individual spring)
and 𝑥 is the distance the spring is displaced
from its equilibrium position

How much force is needed to compress a
spring 12 cm if the spring constant is 84 N/m?

Stretching or compressing a spring also
generates elastic potential energy
1 2
U s  kx
2

How far must a spring with a spring constant
of 444 N/m be compressed to produce an
elastic potential energy of 8.25 J?


Read Chapter 14
Page 378 #1-5



You will be assigned to a group.
Your group’s goal is to experimentally show how each of
the following affect the period of an oscillation (the time
it takes to complete one cycle).
◦ The mass at the end of the string
◦ The length of the string
◦ The angle of oscillation (keep ≤ 45° from vertical)
Materials allowed:
◦
◦
◦
◦
◦

String (and scissors to cut the string)
Masses
Rulers/Metersticks/Protractors
Stopwatch (cell phone)
Tape
Be sure to record everything (procedures and
data)

Leader:
◦ Keep group on task
◦ Collect and return supplies
◦ Determine who performs each part of the lab
(timing, etc.)

Procedures recorder:
◦ Write down everything that your group does
(whether it ends up working or not)

Data recorder:
◦ Write down all data

Helper (2nd period only):
◦ Fill in for any absent group member(s)
◦ Assist group members as needed.
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Group 7
Group 8
Group 9
Procedures
Leader
Recorder
Data Recorder
Le, Dylan
Luu, Justin
Suri, Anirudh
Harris,
Kim, Younghoon Samantha
Remigio, Allexa
Manam,
Bantigue,
Wong, Gracie
Abhinav
Alanna
Yue, Linton
Sitapati, Kedar Roos, Spencer
Nguyen, Austin
Bey, Jack
Swartz, Erika
Townsend,
Herring, Grace
Ton, Tyler
Jaren
Kim, Sean
Clarke, Jacob Wadhwa, Sahil
Marasigan,
Jewell,
Emmanuel
Howo, Michael
Katherine
Hill, Megan Julazadeh, Hana Hill, Megan
Leader
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Group 7
Group 8
Bhushan,
Somil
Procedures
Recorder
Data
Recorder
Helper
Sandfer,
Gupta, Mihir Kye, Johanna
Connor
Laudenslager,
Wedge,
Pennington,
Kapoor, Pia
Alexis
Lauren
Julia
Lodge, Grace Lee, Rudolph Hagstrom, Erik Folkl, Julia
Obermiller,
Nguyen,
Nguyen, Haley Rao, Ananya
Andrew
Wendy
Almond,
Hardisty,
Sharma,
Thomas, Zoe
Amber
Sabrina
Amitesh
Nagelvoort,
Andersen,
Calkins,
Castaneda,
Christopher
Blake
Nicholas
Ernesto
Padmanaban,
Yang, Jerry Kwan, Crystal Imler, Carson
Sneha
Jones,
Waldman,
Brana, Jennifer
Cameron
Philip
A spring is compressed by a 22 N force,
giving it a potential energy of 2.016 J.
a) What is the spring constant of the spring?
b) How far was the spring compressed?


How does mass/length/angle affect the
period?
◦ No effect?
◦ Linear effect? If so, what is the equation of the line?
◦ Non-linear effect? If so, what function is it
(exponential, logarithmic, quadratic, etc.)?

Combine your results to write an equation for
the period in terms of mass, length, and
angle.
◦ The equation may also include constants.
◦ Compare your experimental result with the
textbook equation. Why are they different?






Must be typed
One copy per lab group
Graphs must be computer generated (such as
with Excel, Google Docs, etc.)
Procedures recorder should type procedures
Data recorder should type raw data
Group should work together on:
◦ Introduction
◦ Graphs and data analysis
◦ Conclusions



You will be assigned to a group.
Your group’s goal is to experimentally show how each of
the following affect the period of an oscillation (the time
it takes to complete one cycle).
◦ The mass at the end of the string
◦ The length of the string
◦ The angle of oscillation (keep ≤ 45° from vertical)
Materials allowed:
◦
◦
◦
◦
◦

String (and scissors to cut the string)
Masses
Rulers/Metersticks/Protractors
Stopwatch (cell phone)
Tape
Be sure to record everything (procedures and
data)

A small marble 𝑚 = 2.75 g is pressed down on
N , causing the spring
a vertical spring 𝑘 = 38 m
to compress 3.0 cm from its equilibrium
position. The marble is released, and the
spring shoots it straight up into the air. How
high above the spring’s equilibrium position
does the marble reach?



Small-diameter mass, called
the pendulum bob
String has negligible mass,
but strong enough to not
stretch appreciably
Undergoes simple harmonic
motion if 𝜃 < 15°



Period is the amount of time for one cycle.
Represented by a capital 𝑇.
Measured in seconds, s.
L
T  2
g



Frequency is the reciprocal of period.
Represented by lower case 𝑓.
Measured in Hertz, Hz
◦ 1 Hz = 1/s
1
𝑓=
𝑇




Does not depend on mass.
Does not depend on amplitude (for 𝜃 < 15°)
Can be finely adjusted, and can make
excellent clocks.
Can also be used to solve for 𝑔.

What is the acceleration due to gravity in a
region where a simple pendulum having a
length of 75.000 cm has a period of 1.7357 s?

What is the effect on the period of a simple
pendulum if you double its length?

What is the length of a pendulum that has a
period of 0.500 s? Let g=9.80 m/s2.

The pendulum on a cuckoo clock is 5.00 cm
long. What is its frequency? Let g=9.80 m/s2.

Resonance occurs when small forces are
applied at regular intervals to an object in
periodic motion causing the amplitude to
increase.

Write down as many examples of resonance
that you can think of.

Examples include:
◦ Pushing someone on a swing
◦ Jumping on a diving board
◦ Wind on the Tacoma Narrows Bridge




Read Section 14.1
Page 379 #6-8
Page 380 #9-13
Read Section 14.2
A spring has a spring constant of 125 N/m. It is
attached to the ceiling and a block is attached to
the bottom. The spring is stretched 20.0 cm.
1) Draw a free body diagram of the block.
2) What is the magnitude of the force that the
spring exerts on the block?
3) What is the weight of the block?
4) What is the elastic potential energy stored in the
spring?





A wave is a disturbance that carries energy
through matter or space
A wave usually does NOT transfer mass, only
energy
A wave pulse is a single bump or disturbance.
Most waves are a series of wave pulses.
Two main types of waves:
◦ Mechanical waves – travel through matter
◦ Electromagnetic waves – do not require matter, can
travel through a vacuum

Examples include:
◦
◦
◦
◦


Water waves
Sound waves
Waves on a rope
Waves on a spring
Mechanical waves require a medium (matter)
through which they propagate (travel).
Three main categories:
◦ Transverse Waves
◦ Longitudinal Waves
◦ Surface Waves



A transverse wave is one that vibrates
perpendicular to the direction of the wave’s
motion
A wave on a rope is an example of a
transverse wave
Simulation



Crest – The highest point
Trough – The lowest point
Amplitude – The maximum displacement of
the wave
◦ The higher the amplitude, the greater the amount
of energy transferred.

Wavelength – The distance between
consecutive crests (or the distance between
consecutive troughs)

Identify which point(s) correspond with each
of the following: crest, trough, amplitude,
wavelength



A longitudinal wave is one whose disturbances
are in the same direction as (parallel to) the
direction of the wave’s motion
Sound waves are longitudinal
Waves from a compressed
spring are longitudinal



Compression – A dense part of a longitudinal
wave
Rarefaction – A low density part of a
longitudinal wave
Wavelength – The distance between
consecutive compressions (or the distance
between consecutive rarefactions)



Surface waves are waves with characteristics
of both transverse and longitudinal waves.
Ocean waves are a prime example of surface
waves.
The paths of individual particles are circular.






The following are all used to measure and/or
describe waves:
Wave Speed
Amplitude
Period
Frequency
Wavelength




Wave Speed – The distance a wave travels per
unit time
Represented by a lower case 𝑣
Measured in meters per second, m/s
Depends on the medium through which the
wave is travelling
x 
v

t T







Amplitude – The maximum displacement of a
wave from its at-rest position
Represented by a capital 𝐴
Measured in meters, m
Depends on how the wave was generated
Does not depend on the wave speed or the
medium
More work must be done to generate larger
amplitude waves.
Waves with larger amplitudes transfer more
energy






Period - the amount of time for one complete
cycle/oscillation
Represented by a capital 𝑇
Measured in seconds
Depends only on the wave source
Does not depend on the wave speed
Does not depend on the medium






Frequency – The amount of
cycles/oscillations per second
Represented by a lower case f
Measured in Hertz, Hz
Depends only on the wave source
Does not depend on the wave speed
Does not depend on the medium
1
f 
T
1
units : Hz 
s





Wavelength – Length of a cycle (distance
between similar points)
Distance between crests (or troughs) of a
transverse wave
Distance between compressions (or
rarefactions) of a longitudinal wave
Represented by Greek letter lambda, 𝜆
Measured in meters
v
   vT
f

Sound waves travel approximately 340 m/s in
air. What is the wavelength of a sound wave
that has a frequency of 170 Hz?
2.0 m

Sound has a speed of 3100 m/s in copper.
What is the wavelength of the wave from
You-Try #6 after it crosses into a copper
medium?
18 m




Read Section 14.2
Page 386 #15-25
Read Section 14.3
Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71,
72, 76, 79, 81
A sound wave produced by a clock chime is
heard 515 m away 1.50 s later.
1) What is the speed of the clock’s chime in air?
2) If the sound wave has a frequency of 436 Hz,
what is the period of the wave?
3) What is the wave’s wavelength?




What happens when a wave reaches the end
of its medium?
When the incident wave reaches the end of its
medium, some or all of the energy is
reflected back as a reflected wave.
Some reflected waves are inverted, such as
waves on a rope with a fixed end (as in the
simulation)



The principle of superposition states that the
amplitude of passing wave pulses is additive.
If pulses are on opposite sides, one amplitude
is negative (adding a negative  subtracting)
The result of superposition is called
interference.





Interference can cause standing waves, which
appear to not propagate.
Example: Rope moves up and down, but no
wave pulses move to either side.
The nodes are points that do not move.
The antinodes are the points that move the
most.
Simulation: Amplitude=20, Frequency=30,
Damping=0, Tension=high-1


Stringed
instruments
depend on
standing waves
to make music.
These standing
waves are called
harmonics.


Often represented by a wave front, a line that
represents a wave crest.
Waves move perpendicular to the wave front,
often represented by a ray.

The law of reflection states that the angle of
incidence equals the angle of reflection




Read Section 14.2
Page 386 #15-25
Read Section 14.3
Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71,
72, 76, 79, 81