It was a trick question – force is measured in Newtons , not kg .

1. It was a trick question – force is measured in Newtons, not kg. Reminder: HW 7 is due Saturday at noon. Reading for Tuesday: will be posted. Quiz Tuesday.

2. Questions to be answered today. • How does a violin (or other stringed instrument) produce sound? • Why do the different strings produce different notes? • How does tuning and fingering and different types of bowing • change the sounds being produced? All musical instruments have something that oscillates back and forth in periodic fashion. (because a tone is air pressure oscillating back and forth) Consider the violin. Each piece of string is like little mass hooked to spring.

3. First think about springs a little bit Start a mass bouncing on a spring ... time Time of one oscillation (Period) Relaxed Spring Position Positive direction Mass • If the spring is stiffer, then … • the time per oscillation will increase • the time per oscillation will decrease • the time per oscillation will remain unchanged Position monitor

4. time Time of one oscillation (Period) Position Mass Mass • If the spring is stiffer, then … • the time per oscillation will increase • the time per oscillation will decrease • the time per oscillation will remain unchanged Fnet Fnet When masses are at rest, forces exert upwards by springs are equal. But if mass is displaced from rest position, stiffer spring exerts greater force (=kx) upwards  greater acceleration  faster turn around timeshorter period higher frequency

5. Start a mass bouncing on a spring ... time Time of one oscillation (Period) Relaxed Spring Position Positive direction Mass • If the mass is heavier then … • the time per oscillation will increase • the time per oscillation will decrease • the time per oscillation will remain unchanged Position monitor

6. Start a mass bouncing on a spring ... time Time of one oscillation (Period) Position Mass Mass • If the mass is heavier then … • the time per oscillation will increase • the time per oscillation will decrease • the time per oscillation will remain unchanged Fnet Fnet If the 2 masses are displaced same amount from rest position, net force up due to increase in spring force will exert be equal  gives smaller acceleration for heavier mass  slower turn around time  longer period  lower frequency

7. Start a mass bouncing on a spring ... time Time of one oscillation (Period) Relaxed Spring Position A B C Positive direction Mass At which time is the kinetic energy of the mass greatest? Answer is B … KE = ½ mv2 … highest velocity! Where does energy go at times A and C? Position monitor Into the spring or gravitational potential energy … Spring energy = ½ kx2

8. Tuning fork -- just like mass on spring, going up and down at certain frequency. low pressure sound waves traveling out high pressure (atoms close) low pressure to computer high pressure hit microphone, it flexes, makes voltage V

9. How violin makes sound- strings oscillate up and down. Make body oscillate in and out, pushes air to make sound waves sound waves traveling out low pressure high pressure (atoms close) low pressure to computer high pressure hit microphone, it flexes, makes voltage V

10. Look at the microphone signal from the big tuning fork. If you do the same for the small tuning fork , what does the signal look like? a. higher frequency b. lower frequency c. same frequency low pressure sound waves traveling out high pressure low pressure high pressure hit microphone, it flexes, makes voltage V Answer is a. Higher frequency, because there’s a smaller mass oscillating back and forth at faster rate. Just like the spring when have a smaller mass vsa larger mass. to computer

11. Now pluck thickest violin string hard near the end of the string. • What will we hear and see with microphone? • Single freq./tone b. Two tones/freqs c. Many tones c. Many tones. sound waves traveling out low pressure high pressure (atoms close) low pressure to computer high pressure hit microphone, it flexes, makes voltage V

12. Now pluck thickest violin string soft in the center. • What will we hear and see with microphone? • Same mix of tones b. Different mix of tones. sound waves traveling out low pressure high pressure (atoms close) low pressure to computer high pressure hit microphone, it flexes, makes voltage V

13. String oscillates back and forth. It’s tied downat each end. The simplest way for the string to flex is like this: But there are also higher harmonics … Fundamental frequency, 1st harmonic 2nd harmonic, twice the frequency, G3 string (in tune) gives the fundamental frequency 196 Hz The 2nd harmonic harmonic on this string has frequency = 2 x 196 = 392 Hz Notice how 2nd harmonic is same as the first harmonic of a string half as long. If string ½ as long, then fundamental frequency would double.

14. A string is clamped at both ends and then plucked so that it vibrates in the mode shown below, between two extreme positions A and C. Which harmonic mode is this? a. fundamental, b. second harmonic, c. third harmonic, d. 6th harmonic node: never moves. A These are snapshots at different times. B C answer: 6th harmonic- there are 6 places where the string is vibrating up and down When the string is in position B, instantaneously flat, the velocity of points along the string is... A: zero everywhere. B: positive everywhere. C: negative everywhere. D: depends on the position. CT17-4 Answer : D. depends on position.

15. A B C A string is clamped at both ends and then plucked so that it vibrates in a standing mode between two extreme positions A and C. Let upward motion correspond to positive velocities. 1 2 3 snapshots at different times. When the string is in position B, instantaneously flat, the velocity of points along the string depends on position. When the string is in position C, the velocity of points along the string is... A: zero everywhere. B: positive everywhere. C: negative everywhere. D: depends on the position. CT17-4 A: Zero Everywhere, all points along the string are turning around.

16. What is making the sound you hear? a. string, b. the wood, c. both about the same, d. the bridge b. The wood. String makes wood vibrate, which moves air to make the sound. The wood can push a lot more air. What will happen if we touch tuning fork to the bridge? a. no effect, b. sound will be muffled (quieter), c. sound will be louder, d. Sound will change frequency/tone c. louder, because now the big wood panel is vibrating- more moving air, louder sound.

17. Pluck string, measure microphone signal. What will we see if we tighten string and do the same thing? a. same, b. faster oscillations, c. slower oscillations. Higher the tension means stiffer spring action … b. tighter string pulls back harder, like stiffer spring makes faster oscillations = higher frequency = higher tone.

18. Why is the pitch of the thinner string higher? • There’s more tension in the thinner string, • There’s less tension in the thinner string • The thinner string has less mass • The thinner string is longer c. The thinner string has similar tension, but larger acceleration because its mass is smaller (Recall: the spring with the lighter mass went faster.) Suppose we put down a finger to shorten the vibrating part of the string. What happens to the pitch produced? a. it’s the same, b. it’s higher c. it’s lower b. faster oscillations = higher frequency.