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)kx 2 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.

The Tones f0f0

OCTAVE

The Strings

FRETS

Take a close look at what the string is actually doing: STANDING WAVES 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 WWhat i ii is standing? WWhat i ii is 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.

Another look at the pulse Rope not moving anywhere

Closer Look Lots of Kinetic Energy Here

Time goes by … Energy Energy

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

T

Adding Waves

The String