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1.3 The Ups and Downs

1.3 The Ups and Downs. Science of Music. Things that go back and forth. Pendulum Mass on Spring. 1.5. 1. 0.5. disturbance. 0. Height. 0. 5. 10. 15. 20. 25. -0.5. -1. -1.5. Time (seconds). Another Graph .. a biggy!. Important Definitions.

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1.3 The Ups and Downs

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  1. 1.3 The Ups and Downs Science of Music

  2. Things that go back and forth • Pendulum • Mass on Spring

  3. 1.5 1 0.5 disturbance 0 Height 0 5 10 15 20 25 -0.5 -1 -1.5 Time (seconds) Another Graph .. a biggy!

  4. Important Definitions The PERIOD, T is the time it takes to go from one condition to the next time that exact condition is repeated. The frequency, the number of oscillations per second, is given by: Example: If T=2 seconds F=1/2 (sec-1)=0.5 per second

  5. Question What is a tone and how do you prove it??

  6. Hemholtz • In physiology and physiological psychology, • he is known for his mathematics of the eye, • theories of vision, • ideas on the visual perception of space, • color vision research, • the sensation of tone, • perception of sound. • In physics, he is known for his theories on the conservation of force, • work in electrodynamics, chemical thermodynamics, • A mechanical foundation of thermodynamics. 1821 - 1894

  7. Siren … a scientific instrument

  8. The Graph

  9. 100 Bottles of beer on the wall …

  10. Resonance (later) Loudness Rotational Speed (Turns/second)

  11. Helmholtz Resonators

  12. Piano Keyboard

  13. Helmholtz’s Results

  14. 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.

  15. 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.

  16. 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.

  17. 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

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

  19. Interesting Facts about Sir Issac • He lived a long and fruitful life. • He died a virgin. • He invented the calculus. • So did Leibnitz. • They fought about it. • Nobody one. • The apple story is probably untrue but if it IS true, Newton also must have invented applesauce.

  20. 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 • When you push on something, that something will push back on you with the same force that you are pushing with. (Action = Reaction)

  21. 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.

  22. Now …. lets look at the MONOCHORD but with an important detour. Dr. Koons will play the monochord for us soon

  23. The Spring

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

  25. Springs Oscillate

  26. Graph

  27. Important Result for a Spring:

  28. So ….

  29. A string is just a spring misspelled!

  30. Concept … Tension

  31. Force = F The Musical String Linitial T 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!

  32. The Guitar Strings

  33. 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.

  34. 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!

  35. 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. • Next time we will examine the monochord and Dr. Koons will show us how we develop (a) musical scale(s).

  36. Octave

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

  38. It has been shown that … More about this when we do the string thing.

  39. HAVE FUN!

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