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