Science of Music Week 2 notes (no pun intended) … well, maybe. Springs and Things Science of Music Week 2 notes (no pun intended) … well, maybe.

We need to try to remember a few things from High School Physics Definitions of acceleration and force. Newton’s Laws Directional Thingys … vectors. Relax … it ain’t that hard.

Velocity (speed) Velocity is the distance you have traveled divided by the time it took you to travel the distance. If you travel the 20 miles from Orlando to Lake Buena Vista in 20 minutes, you have traveled speed = 20 miles/20 minutes = 1 mi/min or 60 miles per hour. On I-4 you would also get a ticket if you could drive that fast.

Acceleration Something that is moving at one speed and then starts moving at a faster (or slower) speed is said to be accelerating. Your car accelerates when you start driving it or when you enter a highway (except for I-4 on occasion). You accelerate if you jump out of the window of a tall building. The acceleration continues until the splat.

Definition If you start at a speed of vinitial and finish at a speed of vfinal and it takes a time “t” to accomplish this, then

Sir Isaac Newton (1642-1727) Didn’t really happen but let’s talk about it.

Newton’s Simplified Three Laws An object moving at a constant velocity will continue moving at that same constant velocity if NOT acted upon by an external force. If an external force acts on an object it will accelerate in proportion to the force. F=ma the mass is the proportionality constant and we have defined it previously. When you push on something, that something will push back on you with the same force that you are pushing with. (Action = Reaction)/

Who cares about Newton?? If Newton’s laws were not correct, there would not be any music!!! We will use this stuff in many places but we will not get to deep into it. See Bolemon (reference list) for more information if you want it. For more … any College Physics Text will suffice.

Now …. lets get back to the MONOCHORD via an important detour.

The Spring

Spring Force Equatiom F=-kx The “-” sign indicates that the force and the displacement are in opposite directions.

Springs Oscillate

Graph

Important Result for a Spring:

So ….

A string is just a spring misspelled!

Concept … Tension

The Musical String Like a spring! Linitial T x T T Force = F x T T The Bigger the angle the more T points UP! The distance “x” is the same sort of thing as the x in F=-kx. ANGLE Like a spring!

The Guitar Strings

Consider Two Situations For the same “x” the restoring force is double because the angle is double. The “mass” is about half because we only have half of the string vibrating.

So… For the same “x” the restoring force is double because the angle is double. The “mass” is about half because we only have half of the string vibrating. k doubles m -> m/2 f doubles!

Guitar Pressing the fret that is in the middle of the string doubles the frequency~ Walla … the octave In general … the frequency is proportional to the length of the string. Somewhat explains the monochord results from last session when we built the scale. Let’s look some more at the consonant intervals that Dr. Koons examined with the monochord as he built the major scale.

Octave

1000 Hz.+ 1273 Hz. (a) (b)

Take a wire (String on Guitar ..) Lstretchl Linitial F Lfinal

It has been shown that …