PSC 1121 – PHYSICAL SCIENCE - Physics Main



PSC 1121 – PHYSICAL SCIENCE

“Physics through Music”

October 18, 2004

STUDY GUIDE FOR EXAMINATION II

OCTOBER 22, 2004

NOTE: Science is something that links the past to the present. It is constructed from past principles and when those past principles are found to be wrong, the construction is changes until it agrees with observation. The material that we used in the first part of this class therefore cannot be ignored while studying for the second exam. Concepts such as force, velocity, acceleration, pressure, position, standards, etc. have been used continuously. If a concept is used in the lectures (5-13) covered by this exam, you should be familiar with them. It is not necessary for you to memorize any equations in the following outline that is in red. These will be provided. If it is not in red, you should remember it.

The Lecture numbers referred to below are the numbers on the website. The address is physics.ucf.edu/~bindell. I hope you have visited this site before now!

SOME STUDY GUIDANCE HAS BEEN PROVIDED IN THE LECTURES. OBSERVE THOSE SUGGESTIONS AS WELL.

Lecture 05 - The origins of music is not covered in the text and you will need to use the lecture notes and your own notes on the discussion. You can find information on the bone flute and on animal chorusing by searching on Google. Check the links on the lecture slides as well. Music goes back quite a bit and the slides review some of this history. Be sure to look at the “sonograms” in lecture 5 because that is how we measure the “harmonic” content of a sound. Harmonic sounds sound well together but the reasons are discussed in a later lecture (below). Review the significance of the bone flute. There is some information in the lecture and more (especially an idea of the controversy that surrounded this artifact) can be found at . The lecture also showed the development of various instruments including the other bone flutes and the Chinese bells. This led to a discussion of the main contributions of Pythagoras and his work on the monochord. Much of this discussion is later replicated when we discuss the modern stringed instruments such as the guitar and the violin. Be sure to know the experiments on the monochord and how the instrument was used to create harmonious sounds. This led to the “fifth”, etc. and to the establishment of the musical scale. Don’t worry about musical notation … we only use it to illustrate how tones are related to each other. be sure to know what an octave is.

Lecture 06 – More of the Same. We discussed more about the bone flute and how it was probably fabricated. We defined the important terms:

Dissonance

Consonance

We also looked at some string issues (length vs. tone). The lecture was also mostly historical. Refer to pages 1-4 in chapter 1 of Johnston for some related materials.

Lecture 07 - This chapter began the serious pursuit of the rules for tones that sound good together. It will occupy us for quite a while. We added the interval of the fifth. You can ignore the fourth for a while. We then discussed (it is in the book) how to create the pentatonic scale … the same one that Mort the Caveman used 40K years ago! We then talked about the music of the spheres, but also about some of the astronomical beliefs that existed. Check out Bolemon, chapter 1, pages 8-12.. The major ideas here were related to the contributions of Helmholtz and his resonators and sirens. Know what the importance of this work was!

We also defined the frequency and period of an “oscillator”:

Period of an Oscillator = time per oscillation

Frequency of an oscillator = number of oscillations per second

f=1/T or fT=1

Lecture – 08 We defined the spring constant k based upon its extension under a force. The defining relationship was

F=-kx

Be sure to know what the meaning of the (-) sign is.

The period of an oscillating mass at the end of a sprig, f , is given by

[pic]

We showed how when you cut the length of a string in half, the value of k doubled and the mass was cut in half, so if the tension was kept constant, the frequency doubled. And so, walah, the octave! This behavior of the string, much like a spring, is what allows the stringed instrument to behave in the way it does. Remember that we did this in class as a demo.

Lecture – 09 - This lecture concentrated on the concept of resonance which we will return to later in the semester. Remember the two spring resonance that we looked at in the demo. We then discussed pressure waves and what how we represented loudness as well as frequency on a graph of pressure vs time. We looked at the pressure vs time curve for an octive and noted how well they fitted together and still remained nicely periodic. We did the same for the fifth. We looked at resonance of a spring under a periodic force being applied at different frequencies. We also watched the Tacoma-Narrows bridge fall into the water because of resonance. Remember that the resonant frequency of an object is the naturak frequency of oscillation

Lecture -10 - Here we returned to understand the concept of energy. We defined work as a force times the distance through which the force acted:

Work = Force x Distance

We also included a review of MOMENTUM from precious lectures

momentum = mv

momentum is “conserved” in a collision (know what that means)

If something hits a wall and bounces back, the wall applies a Force over a period of time that changes the momentum of the particle. Momentum is ONLY conserved when there are no external forces. So,

F t = change of momentum = 2 x initial momentum (know what this means!).

This force of the object on the wall was related to PRESSURE (Force/Area) that we discussed in the previous exam period.

The kinetic energy of an object is

KE = (1/2) mv2

and we then decided that ENERGY IS CONCERVED, meaning that the total energy before a collision is equal to the total energy after the collision. Consequently sound from a crash takes some energy away from the total. We call this noise, but if a drum stick hits a drum, it becomes something related to music.

We then LIFTED an object from an initial reference level to a final level and called the energy POTENTIAL energy. Based upon the definition of how much work is done on an object when it is lifted through a height h, we defined the PE as:

PE = mgh

and PE counts in the energy conservation equation!

So the energy before a collision of an object (KE + PE) = total amount of energy available after the collision (KE + PE + losses due to heat, friction, sound, etc.)

Remember the race of the little car and how we applied conservation of energy to the problem. We also dropped an object directly and along a sloped road. In both cases the initial Potential Energy was changed into the SAME amount kinetic energy (no friction).

The potential energy of a SPRING was found to be

[pic]

We discussed that in the oscillation process, the object continuously swaps kinetic energy for potential energy.

The period of a pendulum was also mentioned:

[pic]

Lecture – 11 - Here we discussed standing waves and waves in general. This discussion actually continues in the next two lectures as well. We discussed the guitar and the parts of the instrument and what they do. The “box” was a Helmholz resonator of sorts.

We looked at waves on strings and we learned that

Velocity of a wave on a string =[pic]

We also discussed what happens to a wave on a string when one end of the spring is fixed. (Check out the pictures.)

We then looked at the standing waves that are possible on a string. Shortly, we will use this to develop a new scale or “temperament” called the JUST scale.

Lecture 12 began a discussion of the stringed instruments since we now had more background to discuss them.. We listened to pure tones and how they were generated in a modern laboratory via s speaker although we postponed how a speaker actually works to the next third of the semester. We discussed the tonal range of various instruments and showed that the guitar simultaneously produces many overtones at the same time and that this is responsible for its unique sound.

Going back to the guitar, we discussed more of its operation and how the scale was defined by the frets on the instrument.

Lecture 14 - This lecture discussed more about the sounds from various instruments. More was discussed about standing waves but this time we discussed HOW they happed to form on a string that is fixed at BOTH ends. We discussed Timbre and how the violin differs from the guitar but is still similar. If we get there, we also discuss the function of the bridge.

That’s it for this test!

On the following page I will list the various sections in the two textbooks that you should be familiar with. Check out the slides for problem lists that I may miss here.

Pages in the Textbook that you should know about.

This does NOT include the chapter pages from the last exam.

We have not exactly covered material in the textbook completely or in any order. The material listed below is approximately what we have covered but in Johnston, some interesting history is also listed. The rule of thumb is, if I didn’t cover the topic in class, it will not be on the exam. As I make up the questions, I will be looking at the lecture notes and NOT either of the textbooks. At least, most of the time!

BOLEMON:

|Chapter |Pages |Problems |

|1 |8-12 | |

|4 |75-76 | |

|5 |92-96 (Just review) | |

|6 |All except forces at an angle. Ignore power until later. |1,4,6”a”,7, |

|15 |280-287 |1,2,3,9,10 |

|16 |300-305 (skip diffraction) |1,2,3,4, |

JOHNSTON

|Chapter |Pages |Problems |

|1 |1-12, | |

|2 |Most of it … what we covered in class | |

|3 |56-67, | |

|4 |86-93,97-100 | |

|Interlude -3 |What we covered in class | |

|5 |131-141,144-151 | |

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