lecture 11 getting down to business….. last time we covered the topic of energy bolemon –...
TRANSCRIPT
Lecture 11
Getting down to business…..
Last Time We covered the topic of Energy
Bolemon – Chapter 6 Problems to try: pg 123 1,2,3 (use energy),
5,9,15,16 Energy is conserved. The energy when a process starts is the same as
the total energy at the end but it could change into various forms.
Springs have potential energy ((1/2)kx2 when they are extended or compressed.
We demonstrated that the string on a guitar behaves like a spring.
During Oscillation (Important for Music)
Conclusions The bigger the mass the lower the frequency.
The bigger the spring constant (stiffer) the higher frequency.
m
k
Tf
andk
mT
kxF
2
11
2
Law) s(Hooke'
The Tones
m
k
Tf
2
11f0
022
12
4
2
1
2/
2
2
1f
m
k
m
k
m
kf
OCTAVE
The Strings
FRETS
Take a close look at what the string is actually doing: STANDING WAVES
NODE
NODE
NODE
NODE
A Flash “Photograph”
“NODE”
What is a “node”???
A point where nothing changes with time.
The fixed end of the string is a node There are associated nodes with
standing waves.
A Closer Look
FIXED BY HARDWARE
ROCKING POINT
How does the thing work?STANDING WAVES
What isis standing? What isis a wave?
DEMO -01
Let’s do the wave.
Demo -02
The rope to the back of the room.
What was traveling along the rope??
The rope didn’t go anywhere. Segments of the rope moved up and
down. This up and down motion means that
each little piece of the rope has kinetic energy.
The pulse moves with a speed v.
v
string aon waveof speedv
tension length
mass
Let
Another look at the pulse
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Rope n
ot m
ovin
g a
nyw
here
Closer Look
Lots of Kinetic Energy Here
Time goes by …
EnergyEnergy
EnergyEnergy
What happens at the other end?
Not fixed at the end???
Guitar String CONSTRAINTS
The string is tight. The two ends are FIXED.
They are always NODES.
Harmonic Wave
Harmonic Wave
Harmonic Wave
vf
v
f
1v
vT
periodT
frequencyf
wavelength
waveof speed
T
Adding Waves
http://www.schulphysik.de/suren/Applets.html
The String