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Waves
Hooke’s Law
Robert Hooke 1678
Felastic = k x
Felastic – elastic force (Newtons)
k – spring constant (N/m)
x – displacement (meters)
Spring Constant
• Measures the stiffness of the spring
• The greater the value of the k means a
stiffer spring because a greater force is
needed to stretch or compress that spring
Hooke’s Law ex:
Fel = k x
k=F/x
#1
k = 1N / 1 cm
K = 1 N /cm
#2
k = 2 N/2 cm
K = 1 N/cm
#1
#2
Plot Hooke’s Law from the previous
information.
What is the spring constant?
Spring Constants
• More information
• Hooke’s Law Problems - homework
Simple Harmonic Motion
A vibration about an equilibrium position (in which
a restoring force is proportional to displacement
from equilibrium)
F and a max
F and a max
v max
The motion of Earth orbiting the
sun is periodic. Is this motion
simple harmonic? Why or why
not?
No; because Earth does not oscillate about
an equilibrium position
What is equilibrium, amplitude,
period and frequency?
Amplitude
The maximum displacement from
equilibrium
Period
The time that it takes a complete
cycle to occur
Measured in seconds
T = 1 / f
frequency
The number of cycles or vibrations per unit
of time
Measured in Hertz ( Hz)= 1 / s
f = 1 / T
What is equilibrium, amplitude,
period and frequency?
What is the equilibrium of the
spring?
Period of a Pendulum or spring
Pendulum
L = length(m)
Spring
M= mass (kg)
T = 2p L/ g
g= gravity( 10 m/s2)
T =2p m /k
k = spring constant(N/m)
Pendulum Ex:
You need to know the height of a tower, but darkness obscures the
ceiling. You note that a pendulum extending from the ceiling almost
touches the floor and that its period is 12 s. How tall is the tower?
What is the frequency of the pendulum?
T = 2p L/ g
(T) 2 = (2 p  L / g)2
T 2 = 4 p2 L / g
L=
gT 2 = 10 m/s2(12s)2
4 p2
4 p2
L = 37 m
f = 1 / T = 1/ 12 = 0.08 Hz
Spring Ex:
A 5 N weight oscillates on a spring that has
a displacement of 45 cm. What is the
period of the spring? What is the
frequency?
k = f / x = 5 N / 0.45 m = 11 N / m
T = 2p m/k = 2p .5kg/ 11N/m = 1.3 s
f = 1 / T = 1 / 1.3 s = 0.77 Hz
Pendulum and Spring Problems
Types of Waves
1. Mechanical – a wave that propogates
through a deformable elastic medium
(needs a medium to travel)
2. Electromagnetic – do not a medium to
travel
Mechanical Waves
Longitudinal waves - Waves move parallel to
the wave direction
EX: Sound Wave
Electromagnetic Wave
Transverse wave - Waves move
perpendicular to the
wave direction
EX: Light Wave
Pulse Wave
Throwing a stone in a pond would be a
pulse
Speed of a Wave
Speed of a mechanical wave is constant for any
given medium
Temperature determines speed
V = f l
V = velocity (m/s)
F = frequency ( Hz)
l=
wavlength ( m)
Wave Speed EX:
A piano string tuned to middle C vibrates
with a frequency of 262 Hz. Assuming the
speed of sound is 343 m/s, find the
wavelength of the sound waves produced
by the string.
V = f l
f=v / l
f = 343 m/s = 1.31
262 Hz
Waves Anatomy
Go to the following website to answer the
questions.
• Transverse Waves
1. Define a transverse wave
2. Draw and label the parts of a transverse
wave
3. Define the parts
Waves Anatomy
Go to the following website to answer the
questions.
• Longitudinal Wave
1. Define a longitudinal wave
2. Draw and label the parts of a
longitudinal wave
3. Define the parts
Standing Wave
Draw a standing wave labeling the nodes
and antinodes
• Make your own standing waves
Harmonics
Draw a 1st, 2nd and 3rd Harmonic
Reflection- Study the animations
to determine the difference
between a fixed and free reflection
• Fixed
• Free
Interference
• 1. Define Constructive and Destructive
Interference
• 2. Adjust the points make a crest and
trough, on the left and right. Hit the run
button and see what happens.
• http://id.mind.net/~zona/mstm/physics/wav
es/interference/intrfrnc.html