Presentation on theme: "Chapter 12 Parts of waves (review) Octaves Stringed Harmonics"— Presentation transcript:
1Chapter 12Parts of waves (review)OctavesStringed HarmonicsHow to produce soundOpen/Open HarmonicsOpen/Closed HarmonicsHarmonics/Fundamentals
2Single wave pulse travels Transverse wavesSingle wave pulse travelsTransverse waves:Transverse waves:The particles of the disturbed medium move perpendicular to the wave motionparticlewave
3Longitudinal waves Longitudinal waves: Longitudinal waves: compression travelsLongitudinal waves:The particles of the disturbed medium move parallel to the wave motionLongitudinal waves:
4Basic Variables of Wave Motion Terminology to describe wavesCrest: “Highest point” of a waveWavelength 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
5Sound- is a wave (sound wave)- Rarefied and compressed regionsLongitudinal waveair molecules move back and forth
6Sound 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 20,000 Hz (high).Infrasonic “sound” waves: below ~ 20 HzUltrasonic sound waves: above ~ 20,000 HzThe speed of sound in air: c ~ 343 m/s ~ 740 mi/hr ~ 0.2 mi/sec. (dry air, 68F)
7Question #1 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 mile2 miles3 miles4 miles5 miles
8Notes and their fundamental frequency Octaves: frequency doubles for each tone**Note** An octave will double in frequency each time and this is different than Harmonics
9For example: Find middle C (C4) on the chart to the right. Middle C has a frequency of Hz, one octave higher is C5 which has a frequency of Hz, two octaves higher (C6) has a frequency of Hz.Middle C can also be the fundamental frequency ( Hz) and this is the 1st Harmonic, the 2nd Harmonic (f = Hz) is the same as one octave higher, but the 3rd Harmonic (f = Hz) is NOT the same as two octaves higher.
10Creating 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 antinodesExamples we’ll talk about this chapter:Standing waves on a string.Standing waves in a pipe (open and closed).
11String Harmonics frequency L 2f1 3f1 4f1 5f1 6f1 L … Length of string; n … harmonic v … velocity of sound
12Standing waves have stationary nodes and anti-nodes L … Length of stringn … harmonic
13Fundamental Frequency String vibrates as a single arc, up and downvelocity antinode occurs at center of stringThis is the fundamental frequency modePitch (frequency of vibration) isinversely proportional to string length
14Harmonics (Overtones) In addition, string can vibrate astwo half-stringsthree third-stringsetc.These are higher-order frequency modesThese modes have higher pitches – overtones
15Harmonics in a String In a string, the harmonic pitches are two times the fundamental frequency (octave)three times the fundamental frequencyetc.These integer multiples are called overtonesA string harmonics will have all harmonics.i.e. 2nd, 3rd, 4th, 5th, etc.
16Producing Sound Thin objects don’t project sound well Air flows around objectsCompression and rarefaction is minimalSurfaces project sound much betterAir can’t flow around surfaces easilyCompression and rarefaction is substantialMany instruments use surfaces for sound
20A wave reflecting off of the boundary At an open boundary: the air bounces moving in and out of the boundary.Demo boundary conditions with string and cablemotions
21Harmonic Vibrations for open-open In addition, column of air can vibrate astwo half-columnsthree third-columnsThese higher-order modes are the harmonicsPitches are integer multiples of the fundamentalOpen/open tube has all integer multiples f,2f,3f,4f,5f OR 1st, 2nd, 3rd, 4th, 5th, etc. (just like a stringed instrument)A open-open tube will have an anti-node at each open end
24Wave reflecting off of the closed boundary At a closed boundary: the wave reflects if it has a high pressure at the wall. The air compresses at the wall and then bounces back.
25Harmonic Vibrations for closed-open These higher-order modes are the harmonicsPitches are odd multiples of the fundamentalClosed/open tube only has odd harmonics (e.g., clarinet) f, 3f, 5f, 7f OR 1st , 3rd, 5th, 7th, etc.A closed-open tube will have a node at the closed end
26Question #2You play an open organ pipe with a length of 1m.What is the fundamental frequency?1 Hz86 Hz172 Hz343 Hz686 HzNow you close the pipe at one end. What will the frequency be then?
27Standing waves or modes in a column of air Question #3Standing waves or modes in a column of airThe motions shown are air speedsOne of these is a pipe that is closed on one end and the other is open on both ends. Which one is which?
28Which one has a lower fundamental frequency? Open/open or open/closed? Question #4Which one has a lower fundamental frequency? Open/open or open/closed?closing end of flute!Open/open open/closed
29Fundamental Frequency review Air column vibrates as a single objectPressure antinode occurs at center of open columnVelocity antinode occurs at ends of open columnPitch (frequency of vibration) isinversely proportional to column lengthinversely proportional to air densityA closed pipe vibrates as half an open columnpressure antinode occurs at sealed endVelocity node occurs at the sealed endfrequency is half that of an open pipe