Vote for the best TA

1. Vote for the best TA • i-clicker-2 • Maggie Baldwin is very good • Maggie Baldwin is ok/needs improvement • Calli Nguyen is very good • Calli Nguyen is ok/needs improvement i-clicker-1 Samrat Dutta is very good Samrat Dutta is ok/needs improvement Ashley Carlton is very good Ashley Carlton needs improvement • i-clicker-3 • Jack Owen is very good • Jack Owen is ok/needs improvement • Zach Vance is very good • Zach Vance is ok/needs improvement • i-clicker-4 • Brad Goetz is very good • Brad Goetz is ok/needs improvement

2. Chapter 9.2 Announcements: Homework 9.2: due Thursday, April 1, in class (Calli Nguyen) Exercises: 9, 10, 11, 12, 14, 15, 16, 23, 24, 31, 32 Problems: 1, 2, 3, 4 - Remember: Homework 9.1 is due Thursday, March. 25, in class Heads up: Midterm 2 is coming up on April 13 • We’ll now cover only parts of each chapter (let me know if you want me to cover something that is not on the list and that interests you): • 5.1 Balloons • 7.1 Woodstoves • 9.1 Clocks, harmonic oscillation • 9.2 Musical Instruments, waves • 10.3 Flashlights • 11. Household Magnets & Electric Motor • 11.2 Electric Power Distribution • 15.1. Optics, cameras, lenses • 16.1 Nuclear Weapons

3. Chapter 9.2 Musical Instruments (waves) Concepts Demos and Objects • waves in a room/stadium • waves in a pipe • a speaker (creating sound) • ear • tuning fork • waves on a string • wave modes (harmonics) • longitudinal waves • transverse waves • traveling & standing waves • waves on a string • waves in an air column • ear and hearing • wave length • frequency/pitch • sound

4. Traveling transverse waves Crest/bump travels Transverse waves: Transverse waves: The particles of the disturbed medium move perpendicular to the wave motion particle wave

5. Traveling, longitudinal waves compression travels Longitudinal waves: The particles of the disturbed medium move parallel to the wave motion Longitudinal waves:

6. Examples of waves (i-clicker-1): Which wave is a longitudinal wave? A. “Bump” traveling down a string:___________________ B. Sound waves:____________________ C. La ola in a stadium (getting up/sitting down):_____________ D. Water wave: ____________________________

7. Basic Variables of Wave Motion Terminology to describe waves • Crest: “Highest point” of a wave • Wavelength l: Distance from one crest to the next crest. • Wavelength l: Distance between two identical points on a wave. • Period T: Time between the arrival of two adjacent waves. • Frequency f: 1/T, number of crest that pass a given point per unit time

8. Sound • - is a wave (sound wave) • - Rarefied and compressed regions • Longitudinal wave • air molecules move back and forth

9. Sound Waves Sound waves are longitudinal waves. They consist of compressed and rarified regions of gas (medium) We can hear (audible) frequencies from about 20 Hz (low) to 15,000 Hz (high). Infrasonic “sound” waves: below ~ 20 Hz Ultrasonic sound waves: above ~ 15,000 Hz The speed of sound in air: c ~ 343 m/s ~ 740 mi/hr ~ 0.2 mi/sec. (dry air, 68F)

10. i-clicker-2 It is a dark and stormy night. Lightning strikes in distance. You see the lighting, then, after ten seconds you hear the thunder. How far away did the lighting strike? • 1 mile • 2 miles • 3 miles • 4 miles • 5 miles

11. Sound waves, hearing and the ear http://www.innerbody.com/anim/ear.html

12. Notes and their fundamental frequency Octaves: frequency doubles for each tone

13. Creating standing waves: • When two waves are traveling back and forth, under the right conditions (right frequency), we can create standing waves. • Standing waves have stationary nodes and antinodes • Examples we’ll talk about: • Standing waves on a string. • Standing waves in a pipe (open and closed).

14. String Harmonics frequency L 2f1 3f1 4f1 5f1 6f1 L … Length of string; T … Tension m … mass of string

15. Standing waves have stationary nodes and anti-nodes L … Length of string T … Tension (not period T) m … mass of string

16. Strings as Harmonic Oscillators • A string is a harmonic oscillator • Its mass gives it inertia • Its tension gives it a restoring force • It has a stable equilibrium • Restoring forces are proportional to displacement • Stiffness of restoring forces determined by • String’s curvature • String’s tension

17. Fundamental Vibration • String vibrates as a single arc, up and down • velocity antinode occurs at center of string • This is the fundamental vibrational mode • Pitch (frequency of vibration) is • proportional to • inversely proportional to string length • inversely proportional to

18. i-clicker-3 • How can a violin player play a lower note: • Increasing the tension in the string. • Playing a string with less mass (thinner string). • Shortening the string. • A & C • None of the above.

19. Overtone Vibrations • In addition, string can vibrate as • two half-strings • three third-strings • etc. • These are higher-order vibrational modes • These modes have higher pitches – overtones

20. Harmonics in a String • In a string, the overtone pitches are • two times the fundamental frequency (octave) • three times the fundamental frequency • etc. • These integer multiples are called harmonics • Bowing or plucking a string tends to excite a mixture of fundamental and harmonic vibrations, giving character to the sound

21. notes E5 A4 D4 G3 • i-clicker-4: • Why do all musical instruments have a body (wood body, metal shell, etc)? • They look prettier • They are easier to hold • They act as resonators (amplify sound) • They act as dampers (reduce sound) • No good reason

22. strings Mouthpiece body Air column Music and Resonance: Primary and secondary oscillators Wind Instruments String Instruments

23. Connecting primary (strings) and secondary (body) oscillators

24. Producing Sound • Thin objects don’t project sound well • Air flows around objects • Compression and rarefaction is minimal • Surfaces project sound much better • Air can’t flow around surfaces easily • Compression and rarefaction is substantial • Many instruments use surfaces for sound

25. Violin Harmonics Viola Harmonics

26. Compare to Chladni plate demo

27. i-clicker-5: Why are some violins so expensive (Stradivarius : $ 1.5 M)? Computer Tomography scan of a Nicolo Amati Violin (1654) • Old stuff is always expensive. • They are made of expensive materials. • In fashion and music, you pay for the label. • The secondary oscillator mixes a rich sound of harmonics. • The primary oscillator produces unusual frequencies.

28. Primary Resonators: Wind Instruments Flute Woodwinds Brass Lips Fixed Edge Reed

29. Open pipe:

30. Fund. Frequency c… speed of sound c = 343 m/s in air

31. Fundamental frequency: Half-closed pipe:

32. i-clicker-6; 7: • You play an open organ pipe with a length of 1m. • What is the fundamental frequency? • 1 Hz • 86 Hz • 172 Hz • 343 Hz • 686 Hz • Now you close the pipe at one end. What will the frequency be then? • 1 Hz • 86 Hz • 172 Hz • 343 Hz • 686 Hz

33. Air as a Harmonic Oscillator • A column of air is a harmonic oscillator • Its mass gives it inertia • Pressure gives it a restoring force • It has a stable equilibrium • Restoring forces are proportional to displacement • Stiffness of restoring forces determined by • pressure • pressure gradient

34. Fundamental Vibration • Air column vibrates as a single object • Pressure antinode occurs at center of open column • Velocity antinode occurs at ends of open column • Pitch (frequency of vibration) is • inversely proportional to column length • inversely proportional to air density • A closed pipe vibrates as half an open column • pressure antinode occurs at sealed end • Velocity node occurs at the sealed end • frequency is half that of an open pipe

35. Harmonic Vibrations • In addition, column of air can vibrate as • two half-columns • three third-columns • four fourth-columns • These higher-order modes are the harmonics • Pitches are integer multiples of the fundamental • Blowing across column tends to excite a mixture of fundamental and harmonic vibrations