10/7/20101It 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.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 bowingchange the sounds being produced?All musical instruments have something that oscillates back and forth in periodicfashion. (because a tone is air pressure oscillating back and forth)Consider the violin. Each piece of string is like little mass hooked to spring. RelaxedSpringMassFirst think about springs a little bit Start a mass bouncing on a spring ... PositionmonitorPositivedirectionPositiontimeTime of one oscillation(Period)If the spring is stiffer, then … a. the time per oscillation will increaseb. the time per oscillation will decreasec. the time per oscillation will remain unchangedMassPositiontimeTime of one oscillation(Period)If the spring is stiffer, then … a. the time per oscillation will increaseb. the time per oscillation will decreasec. the time per oscillation will remain unchangedMassFnetFnetWhen 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 frequencyRelaxedSpringMassStart a mass bouncing on a spring ... PositionmonitorPositivedirectionPositiontimeTime of one oscillation(Period)If the mass is heavier then … a. the time per oscillation will increaseb. the time per oscillation will decreasec. the time per oscillation will remain unchangedStart a mass bouncing on a spring ... MassPositiontimeTime of one oscillation(Period)MassFnetFnetIf 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 frequencyIf the mass is heavier then … a. the time per oscillation will increaseb. the time per oscillation will decreasec. the time per oscillation will remain unchanged10/7/20102RelaxedSpringMassStart a mass bouncing on a spring ... PositionmonitorPositivedirectionPositiontimeTime of one oscillation(Period)At which time is the kinetic energy of the mass greatest? ABCAnswer is B … KE = ½ mv2… highest velocity!Where does energy go at times A and C? Into the spring or gravitational potential energy … Spring energy = ½ kx2Tuning fork -- just like mass on spring, going up and down at certain frequency.sound wavestraveling outhigh pressure(atoms close)high pressurelow pressurelow pressurehit microphone,it flexes, makes voltageVto computersound wavestraveling outhigh pressure(atoms close)high pressurelow pressurelow pressurehit microphone,it flexes, makes voltageVto computerHow violin makes sound- strings oscillate up and down.Make body oscillate in and out, pushes air to make sound wavesLook 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 frequencyb. lower frequency c. same frequencyto computersound wavestraveling outhigh pressurehigh pressurelow pressurelow pressurehit microphone,it flexes, makes voltageVAnswer 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 vs a larger mass.sound wavestraveling outhigh pressure(atoms close)high pressurelow pressurelow pressurehit microphone,it flexes, makes voltageVto computerNow pluck thickest violin string hard near the end of the string. What will we hear and see with microphone? a. Single freq./tone b. Two tones/freqs c. Many tonesc. Many tones.sound wavestraveling outhigh pressure(atoms close)high pressurelow pressurelow pressurehit microphone,it flexes, makes voltageVto computerNow pluck thickest violin string soft in the center. What will we hear and see with microphone? a. Same mix of tones b. Different mix of tones.10/7/20103But there are also higher harmonics… 2ndharmonic, twice the frequency,G3 string (in tune) gives the fundamental frequency 196 HzThe 2ndharmonic harmonicon this string has frequency = 2 x 196 = 392 HzNotice how 2ndharmonic is same as the first harmonic of a string half as long.If string ½ as long, then fundamental frequency would double.Fundamental frequency, 1stharmonicString oscillates back and forth. It’s tied down at each end. The simplest way for the string to flex is like this: 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. 6thharmonicWhen 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.ABCanswer: 6thharmonic- there are 6 places where the string is vibrating up and downThese are snapshots at different times.Answer : D. depends on position.node: never moves.ABCA 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. 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.1 2 3snapshots at different times.A: Zero Everywhere, all points along the string are turning around.What is making the sound you hear?a. string, b. the wood, c. both about the same, d. the bridgeWhat 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/toneb. The wood. String makes wood vibrate, which moves air to make the sound. The wood can push a lot more air.c. louder, because now the big wood panel is vibrating- more moving air, louder sound.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