“Physics through Music”



“Physics through Music”

Examination Review

December 4, 2004

What have we covered in the books? (Notice that not all material comes from the textbooks so you need to review the lecture notes as well.) There is a lot of relevant information at

You will have to search for the right topics.

|General Topics |Johnston |Bolemon |Bolemon Problems |

|Music Stuff to Read |Chapters 1,2 | | |

| |Interlude I , pages 41-47 | | |

|Some of this material comes from|Chapter 3, most of it | | |

|previous work. This material |Chapter 4, 88-100 | | |

|will be completed before the |(remainder of the chapter is | | |

|next exam. |interesting) | | |

| |Chapter 5 all | | |

| |Interlude 4,152-166 | | |

| |Chapter 6,178-180, 183-191 | | |

| |(not all covered in class) | | |

| |Chapter 7, 221-244 | | |

| |Interlude 6, 247-260 | | |

| |Interlude 8,319-338 | | |

| |Appendix 2,4 | | |

| |Chapter 8 268--286 | | |

|Chapter 1 | |Pages 16-17 |19-21 |

|Chapter 6 | |All of chapter except forces at |Same as before. We actually |

| | |angle |covered this on the previous |

| | | |test but you still need to |

| | | |understand energy. |

|Chapter 15 | |Through Pg. 290 |1-7 |

|Chapter 16 | |Pg 300-305,308-312 |1,2,4-6,11,12 |

|Chapter 17 | |Pg 318-324,328-330, |1-7 |

|Chapter 18 | |Pg. 338-351 |most |

|Chapter 19 | |Pg. 356-363 | |

|Chapter 20 | |Pg. 382 | |

The relationships between frequency, period and wavelength should be recalled from the material covered on the last exam. It clearly applies to the new material. Most of the new material is more qualitative in nature so that not too many (if any at all) formulas have been introduced.

You are expected to have read all of the material described in the table above and you should be able to reproduce the salient features. Concentrate on material that I covered in the classroom. This will be what will be stressed on the exam.

There will be no formula sheets used for this exam since there were only a few formulas. What you need will, except for the most obvious cases, will be supplied as a part of the question.

The material covered on this exam is reflected by Lectures 13-22, all of which appear on this website. The highlights of each of these lectures are as follows.

Lecture #13

This lecture was a completion of the previous discussion of the guitar. Note that standing waves were once again stressed (read about how they are formed in Johnston). The function of the bridge as well as the timbre of the instrument was covered briefly. The extension to the violin then took place. Make sure that you fully understand the last slide (What happens when …) of this lecture. Know what it means and how to interpret it. What are the wavelengths and frequencies for each diagram?

Lecture #14

Again we discussed the frequencies that were stable on stringed instruments. I must think this to be an important topic. We discussed how toned are added and how the fifth looks as compared to an interval not quite a fifth sounding together. Consonance was started here with two consonance curves being presented which will rear their ugly heads in a later lecture.

Ptolemy’s contribution of the “Just Scale” was covered here and in the next lecture. Note the complex instrumentation required because the Just scale didn’t allow for the change of musical keys. This let to equal temperament. Know what the scales were if not exactly how to calculate either the frequencies of either one.

Lecture #15 included the results of test #2.

Again, the musical scale was described leading to a discussion of the flute. This material is well covered in the Johnston text. Understand where the nodes and antinodes are for resonance and understand the pressure node vs. the velocity node. They are different and some graphs appear that point out the differences. Both closed and open ended tubes (flutes) are important here and in the lectures on voice.

Lecture #16

This lecture discussed the resonances and the modes of vibration of an instrument. Understand the three guitar figures … the vibration modes as well as the tones that come out. Can you calculate the frequency and wavelength or period from the figure labeled “Sound from the Guitar”? You should be able to. We then discussed the modes of vibration of the bar and the drum and pointed out that the drum is NOT harmonic. But the drum has clear vibrational modes. Diagrams are included.

Lecture #17

The next topic concluded drums and jumped into some physics of power. Power was defined and we discussed how the power per unit area decreases with the square of the distance from the source. We calculated how much energy per unit time per unit area arrives at the ear from a sound source a distance away from it. Know how to do this.

You also should know what a log is and be able to work with powers of 10 (although the treatment will be minimal, if at all). Know the definition of the decibel. Know what the acoustic power is and the range of human hearing.

Lecture #18

Again, power is stressed with some overlap of log, dB and range of hearing. We also cover the frequency range of hearing and you should know the salient facts. Know the limits and the sizes of things. What is the minimal level of hearing? The threshold of pain. The dynamic range between them.

We then turned to the major parts of the ear. Know how the cochlea deciphers the frequency from the sound the ear receives. Know about the damage that can occur from loud music and the role of the hair cells.

Lecture #19

We continued with hearing and stressed how the basilar membrane works and what it does. We then jumped into the processes that take place between the source of sound and the ear. Know about reflection, absorption, interference, diffraction, phase differences and finally, beats.

Lecture #20

More of the same. Review “Consider this Table”, roughness, and how the old amphitheaters were designed. The band shell is another example. How does the “whispering gallery” work? The parabolic receiver?

Huygen’s principle allows the understanding of diffraction (well, …) and we looked at what happens with small holes in walls vs. larger ones. Next we jumped into room dynamics and discussed reverberation, how it is measured and how the various properties of the room determine the reverberation time. We looked at the reflective (or absorptive) properties of various materials and finally what reverberation times are needed for various types of performance. Rock bands were not included.’

We then finished up the consonance material. The book is pretty good on this stuff. A quick review of the cochlea shows how important this topic really is! Finally, a trip to the brain and we had music. Beethoven, in particular.

Lecture #21

No need to review this section since it was stolen completely from the textbook. Understand how the voice is produced by a combination of resonance, puffs of air and the Fourier Theorem that was discussed previously. Know how the vocal folds work (remember that funny noise??).

Recognize how the volume of the room and the absorption of the walls effect the reverberation time.

Lecture #22

The Human Voice was discussed here. Know how the tone (frequency) is produced and where in the “vocal tract” it comes from. The function of the lungs, vocal chords, etc. in voice production. Fourier’s Theorem raises its ugly head again. Do you know it yet? Types of voice and rough frequency ranges. Hey guys … wanna be a castrato? What was this and why was it a good career in those days?

Make sure you know about open tubes and the notes and the frequencies that can be produced by such a structure.

Lecture #23

Most of this is in the Bolemon text. The nature of dead cats and their contribution to understanding electricity. Charges, two types, and how they interact. Moving charge is the negative electron. Know what induction is and why the charged rod moved a neutral 2 x 4 board.

Lecture #24

We finished charged objects and introduced Coulomb’s Law for the force between charges. Know that it is an inverse square law. We looked at balloons, bits of paper and how they were effected by static charges. We discussed types of materials as well … insulators and metals. We touched on the Van der Graaf machine and demonstrated how it works. We only lost one student.

Lecture #25

Again, mostly in the book. We discussed capacitors, batteries, and resistors. OHM’S LAW (very important). We discussed circuits with light bulbs (there is a question on this). The music application here was the beginning discussion of loud speakers and how they work.

Lecture #26

Magnetism and how currents are made with wires moving through magnetic fields. We looked at magnets, N & S poles. Where does the compass point?? What is a dynamic microphone?

Lecture #28

We finished microphones and discussed amplifiers, the electric guitar and how it works and began to wrap things up.

Lecture #29

The last things we discussed was the synthesizer and final digital applications of electronics to music and recording. The CD and a little about how it works. MP@ … what is it? What is a “bit”?

That’s about it. Be sure to review the early stuff about “Supe” and how he handled his girlfriend’s falling problem. How do things fall, acceleration, gravity.

GOOD LUCK

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