Physics Test #3

Instruments that act like an open-open (Harmonics)

Flute Saxophone Oboe Trombone Every brass instrument Trumpet (has all harmonics except for one- it has a missing fundamental) -Mostly cylindrical but acts like open-open

Keys

88 keys, 36 black, 52 white

Inharmonicity (of Piano Strings)

A condition in which overtones are not harmonics of the fundamental frequency They play a very important role in the sound of the piano, because there is some inherent stiffness in the strings and therefore the overtones produced do not have the simple integral relationship of the harmonics we learned in the past. This inherent stiffness makes the overtones too high, as if oscillations were a more tightly stretched string. The higher overtones result from modes in which the string has many loops and thus a great deal of bending, and these are successively higher in pitch than the simple harmonics of 2f,3f, etc..

Damper

A soft rectangular block that rests on piano strings to prevent their vibration, so when you press down the sustain pedal, it takes off the dampers which allows the strings to vibrate for longer

Difference in tuning for piano and harpsichord

As you tune up higher and higher you have to match the harmonics, the two C's on opposite sides of the piano will not sound as if they are in tune To tune a harpsichord you can adjust the tension of the strings

What is the main function of the bell? (Recall the garden hose "hose-a-phone" demo)

Bell provides the proper coupling (or impedance "match") between the instrument and the outside air to transfer sound most efficiently and make sound louder. It also modifies the frequencies and stability of the resonances (especially the lower ones) Most obvious effect of the bell is to increase the volume of sound from the instrument Place hand in bell → darkens the tone Garden hose "hose-a-phone" demo- take a garden hose and out a funnel in it → makes things louder Funnel allows you to match impedance

Know the effects that the flared bell and mouthpiece have on the frequency spectrum of the instrument

By varying the size and shape of the mouthpiece and the flare and length of the bell, the frequencies of the resonances can be adjusted to most nearly match the harmonics of the overtone series (except the fundamental) Flaring the bell changes the frequencies of impedance peaks (affects timbre) and changes height of impedance peaks (emphasizes different overtones) → more directional sound at high frequency

Know the basics of Bernoulli's Principle (faster flow= lower pressure)

Changes height of impedance peaks (emphasizes different overtones) Spectrum of radiated sound changes Losing impedance peaks at high frequency = bigger peaks in radiated sound spectrum at those frequencies (energy can get out more easily!) More directional sound at high frequency Pressure node can vary in location (does not have to be at end of bell)

Instruments that act like a closed-open (odd harmonics)

Clarinet Any cylindrical woodwind Coronet (small trumpet) vs. clarinet

Function of a bridge in a violin

Conducts vibrations from the strings to the body

What does a sound post do?

Conducts vibrations from the top plate to the bottom plate and keeps it from collapsing or caving in

Know the basic differences between conical and cylindrical bores

Conical bores- overblowing at the octave (integer multiple of fundamental).. I.e. saxophone, oboe, etc. Cylindrical bores- overblowing at the twelfth (odd-integer multiple of fundamental).. I.e clarinet

How do their frequency spectra differ? (conical or cylindrical)

Conical woodwinds are all harmonics (open-open harmonics) Saxophones → spectrum includes both odd-numbered and even-numbered harmonics (because it is conical and therefore encompasses all harmonics) Cylindrical woodwinds/ clarinet are going to be odd harmonics

Know how conical bore instruments differ from cylindrical bore instruments

Cylindrical bore brass instruments: are those in which approximately constant diameter tubing predominates. Cylindrical bore brass instruments are generally perceived as having a brighter, more penetrating tone quality compared to conical bore brass instruments. The trumpet, and all trombones are cylindrical bore, and clarinet. Act as closed-open pipes. Thus, λ1= 4L (odd harmonics only) Conical bore brass instruments: Conical bore brass instruments are those in which tubing of constantly increasing diameter predominates. Conical bore instruments are generally perceived as having a more mellow tone quality than the cylindrical bore brass instruments. Tuba, saxophone, conch shell, alphorn. Act as open-open pipes and have fundamental wavelength that is twice the pipe's length (λ1= 2L) → all harmonics present

Are double-reed instruments usually conical or cylindrical?

Double-reeds are conical tubes with the tip of the one removed and a reed attached → generally overblow at the octave, but generally it depends Double reeds function acoustically in the same manner as single reeds; the tone quality of most reed instruments depends much more strongly on the size and shape of the bore. There are some differences in detail that will be discussed as each of the instruments surveyed Example/ Bassoon (2 reeds that are pressed together)

Know the effect of the register key, and how it affects the pressure nodes/antinodes in the clarinet's air column

Effect of the register key- allows you to excited the next possible higher harmonics (for the clarinet, the next allowable harmonica has a frequency 3 times the fundamental (thus an octave and a fifth above the note played normally)) Fundamental mode displacement node at closed end and antinode at open end -- by venting the tube at one-third of its length from the closed end, an antinode is forced at that position Register key provides the venting to force an antinode over a wide range of notes

What is meant by an air reed?

Flute - no actually piece of wood that moves back and forth (also organ pipes) A woodwind sub-class → Flutes are air reeds (player is in direct control of the angle at which the air from the lips strikes the holes) A free reed aerophone is a musical instrument that produces sound as air flows past a vibrating reed in a frame. Air pressure is typically generated by breath or with a bellows

Is a flute treated as a pipe open at both ends, or as a closed-open pipe?

Flute acts as open-open pipe

In which case can the player control the frequency?

For a woodwind instrument with a reed, the player blows the instrument directly through a hole in the box enclosing the reed but without touching the reed with the lips, a technique that permitted considerably greater control of the tone, articulation, and intonation than in the bagpipe. On the other hand, an even greater degree of tone control was obtained by removing the cap and blowing the instrument directly with the lips n the reed. Player can control the frequency with brass reed (lip) vibrations

What is Helmholtz motion?

Helmholtz motion for a violin- the disturbance that goes around in a string entirely different than Helmholtz resonator Bow drags string in same direction→ forced kink at spot of bow and it will eventually slip under the tension of the kink When it snaps back into place, the kink moves back along the string until it hits the top of the neck and then reflect back As the kink of the string goes around→ that is called the Helmholtz motion Once it makes a full trip down and back, it will cause the string to move against the bow again→ creates the same pitch as if you were to pluck the string at the same point

What is Helmholtz resonator?

Helmholtz resonator is the body of the violin. They have to be a bottle with a volume of air, with a neck. For example a pipe or a recorder. (Example/ Bottle, with some opening where the neck is, with air inside)

Know why bowing a violin closer/farther from the bridge changes the frequency spectrum produced and what the nature of those changes are

If the bow is moved closer to the bridge (nearer the end of the string), the N value will be greater and the tone will have more harmonics. =Sul ponticello If the string is bowed farther from the bridge (closer to the middle of the string), the N value will be less and fewer harmonics will be produced =Sul tasto By moving the bowing point along the string, the player can produce either a richer or a more mellow tone → position at which bowed affects harmonics produced

How are wavelength and frequency affected by changes to various quantities like tension, mass per unit length, etc.?

If you have a wave on a string, the speed is able to be calculated V = wavelength x frequency I f you change tension or mass per unit length, changes wavelength or frequency Increase tension, frequency increases → What doesn't change? Mass per unit length and wavelength

Know why the placement of electric picking on an electric guitar will emphasize different harmonics of the sound spectrum

If you pick close to the bottom end, you will get a lot of high frequencies/harmonics, if you pick closer to the third harmonic (antinode) Pick close to edge → high harmonics, picking at a normal spot → normal highmonics Electronic pickup convert the sound vibration into an electronic signal. This signal is then fed into a preamplifier and power amplifier, and then to a speaker system. Uses direct electromagnetic induction Signal generated is too weak to drive a loudspeaker, so it is amplified first Can easily be altered because the output is an electrical signal... electronic circuits add "color" to the sound → signal can be modified using special effects such as reverb and distortion

What is the purpose of the sound board?

It is an amplifier which moves a lot of air. It also acts as a resonator (making sound louder) and it is where sound radiates. It is made of spruce planks joined together, lightweight wood it is bellied upward, and it fits tight into the case. The soundboard sits under the heavy cast iron frame.

Be able to describe how pressure pulse can reflect at the open end of the instrument and return to the mouthpiece, affecting the motion of the reed

It is possible for the reed of a clarinet to "lock in" with the air column by vibrating three times as fast Reed would close, open, and close again during one round trip of the pressure pulse Thus is ready to receive a "pull" when the negative pulse returns Can be accomplished with higher embouchure pressure and (usually) an open register key Reed then vibrates at a frequency three times that of the fundamental There is a wave that reflects back, if you send a high pressure wave out there, a wave comes back High pressure pulse that goes to bell → continues out, there is a gap that opens up... gap travels back and reflects back

Know about the "Rule of 18" for placing frets on a stringed instrument like a guitar

Keep taking 17/18th's away (each is about 6% of string) → ratio of string a half step apart is 18:17 -Once you are halfway, frets are closer together The first fret is placed 1/18th of the distance from the nut at the top of the neck, to the bridge. Then, each additional fret is placed 1/18th of the remaining distance. This rule helps you place the frets and explains why they are closer together as you go further down

Mersenne's Law

Laws that define the fundamental frequency of a stretched wire in terms of its length, tension, and mass per unit length.

Una corda (Pedals)

Left piano pedal ("soft" piano pedal) It allows only two of the three strings for each note to be struck, reducing the prompt sound but not the delayed sound. When the pedal is pressed, the entire keyboard and action are shifted slightly to the side so the hammer that would normally strike 3 stings, only strikes 2 strings. The 2 struck strings would begin moving in phase and start to drive the unstruck string to move out of phase. The sustained sound will occur before the amplitudes of the struck strings have dropped very much. The sustained sound is louder, relative to the prompt sound.

Know how the fundamental frequency and harmonics depend on the length of the instrument

Longer instruments will have a longer fundamental If you have something that acts as an open pipe, then the fundamental will be wavelength / 2L Odd → 4L, 4L/3, etc. How does it relate to the length of the pipe The bore is shaped to preserve this harmonic relation as the finger holes are opened; in other words the harmonicity of the overtones must remain stable as the effective length of the instrument is changed. The only two bore shapes that are physically possible to produce and play are the cone (area is proportional to the square of the distance from the pointed end) and cylinder (area is constant) The length of the instrument is that ½ of the wavelength C equals L between the fipple opening and the bell. When all the holes are open, the effective length is L/2, one-half of the original wavelength, producing twice the original frequency

What is a "popping frequency"?

Lowest resonance frequency of the brass mouthpiece itself -sound spectrum enhanced at this frequency It will tend to bring lower harmonics up

Body/Case of the piano

Made out of wood veneer and now plastic, layers of wood on top of one another that becomes one piece and is bent around, rock maple (piano guy)

What happens to the pitch if the opening hole is Made larger?

Making a hole larger allows the air to flow in and out more easily, moving the antinode up, and thereby shortening the wavelength and raising the pitch

What happens to the pitch if the opening hole is Made smaller?

Making a hole smaller lowers the pitch

Sustain Pedal

Middle pedal It lifts the dampers to allow the strings to vibrate freely. This pedal sustains only keys that are being held at the time the pedal is pushed. It acts as a damper pedal for the notes in the low range. This is useful for some types of music in which chords must sound while both hands play other notes.

What happens to the pitch if the opening hole is placed closer to the blow end?

Moving a hole upward closer to the mouthpiece decreases the length of the standing wave and increases the pitch of the note controlled by that hole

Know how to determine wavelengths and frequencies of closed and open pipes (a review of chapter 3.4 may help)

Open pipe: Determine wavelength: ƛ = 2L Determine frequency: f = S/2L Closed pipe: Determine wavelength: ƛ = 4L Determine frequency: f = S/4L

Know how changing the length of an instrument affects its fundamental frequency

Opening extra lengths of tubing gives other notes that are not in harmonic series Changing length affects fundamental frequency -If length gets longer, frequency and pitch go down

Frequency in Marsenne's Law

Proportional to the square root of string tension Inversely proportional to string length Inversely proportional to the square root of the string's thickness It is used to understand the most obvious features of piano strings. The first is that the strings of high notes are shorter than those of lower notes. The mass per unit length is changed in accordance with Mersenne's third law, to make the pitch of the lower strings low while keeping the length reasonable. The tension does not vary significantly from string to string because that might lead to uneven stress on the frame and buckling. The weight is added in the form of multiple wrappings of the wire→ lower strings are wrapped in copper wire, and the very lowest strings have two of such wrappings

How can a recorder be made to play chromatic notes even when they have not been technically included on the instrument? (Hint: Can holes only be closed or open, or is there an in-between option?)

Recorder → "open-open" pipes, behaves like an open tube Tone-holes → facilitate reaching the lowest tone-hole Chromatic notes are played by finding the most accurately tuned fork fingerings → "force" the positions of the antinodes to the proper location, resulting in a tone that is different in quality from diatonic notes Necessary to further modify the hole sizes and positions to tune chromatic notes In between option??? If there is a hole that is smaller, you can put it on a different place in the recorder to get the same note If you make it smaller and leave in same place, less effect on pitch If you partially open it, might raise the pitch less → a way to make a smaller hole on the instrument without actually drilling a hole

Know why the "reed" and "flute" make up the two different categories of woodwinds (He is referring to a reed pipe and a flute pipe)

Reed pipe: An organ pipe that uses vibrating reed to produce sound (i.e. clarinet, saxophone (single reed) or oboe, bassoon (double reed)). Sound nasal and buzzy. Flute pipe: An organ pipe that uses an edge tone for sound production. (flute, piccolo, recorder, etc.). Reed: The oscillating air column drives the reed at the resonant frequency of the standing wave in the tube. Flute: The bigger the woodwind instrument, the lower the pitch they make. Flute instruments make sound when the musician blows air across the eds in the instrument while reed instruments have a reed or two that vibrate when the air is blown

What is fundamentally different about the frequencies that can be produced by woodwind reed vibrations vs. brass reed (lip) vibrations?

Reed: natural resonant frequency is a set value Aka the "squeak" frequency (thousands of Hz) We need the pipe to force the reed to oscillate at the frequency we want The body of a woodwind instrument forces the reed to vibrate at the body's resonant frequency Lips: resonant frequency is adjustable

What effect does the cylindrical bore have on the resonance frequencies?

Resonance at fundamental + odd integer multiples It takes odd harmonics and makes them open-open harmonics, so that you have all of the harmonics

What is the bass bar in a violin?

Responsible for emphasizing lower vibrations (It makes the violin louder at those low frequencies). It would be located in the inside, on the underside of the top plate

Are saxophones conical or cylindrical?

Saxophones are conical bore

Know why a secondary oscillate (guitar body, violin body, etc.) is necessary for string instruments (as well as what serves as the primary oscillator)

Strings are causing all sorts of vibrations and the faceplate will emphasize different ones depending on the faceplate vibration The string is the primary oscillator

Know what is meant by "tap tuning" for a violin faceplate

Tapping on a violin plate and seeing where the sand piles up (seeing what the resonant frequencies are) Frequency of the wood resonance is determined by the violin maker through tap tones As the plate is made thinner, the tap tone becomes bell-like and attains correct frequency

How does opening a tone hole affect pitch (does it raise or lower the frequency played?)?

The finger hole opens to allow the air to come in and out, effectively moving the antinode from near the bell end to near the position of the first open hole An open tone hole will shorten the acoustical length of the tube.

Hammer

The hammer is the part of the piano mechanism that strikes the string to produce vibrations

Piano strings

The heart of the piano

What happens to the pitch if the opening hole is placed farther from the blown end?

The hole spacing increases for holes farther down the tube from the fipple and the pitch is lower

Difference between highest and lowest notes in piano and harpsichord

The strings of higher notes are shorter and thinner than the strings of lower notes Lowest note is at the far left of the instrument and the highest note on the far right. These 88 pitches, generally speaking, are all the ones our human ears can recognize as musical sounds. Pitches lower than the bottom note of a piano: the low 'A', are so low as to sound like a rumble; any note above the highest note on a piano. the high C, can be heard only by plucky dogs.

Should a brass instrument be considered an open-open or open-closed pipe? Does that match the harmonic series produced by the instrument? How do we resolve the difference? (Consider where the pressure varies greatly and where it has essentially no variation from atmospheric pressure)

They act like open-open pipes, conical, because it has the harmonics of an open-open, but it really is a closed-open pipe. The conical shape is the way to resolve this, because conical pipes should not usually have all of the harmonics Closed-open pipes have odd-integer harmonics but how do we make these integer harmonics? Bell and mouthpiece Bell end, opens to outside world so it needs to match atmospheric pressure (pressure node) Pressure varies greatly where the lips are (pressure antinode)

Know what Helmholtz motion is for a bowed string

When string is bowed with great pressure, the very-large amplitude oscillations elongate the string and cause an increase in the tension of the string.. This increased tension leads to a rise in the frequency of the string (due to Mersenne's law) Thus, bowing a string with great pressure causes a rise in pitch Forcing a kink at a certain spot in the string → tries to snap back as a result of creating a wave that goes around string kink slips from bow and continues around... as kink goes around, it travels at same speed and causes bow to catch string again (repeated slipping and sticking → same pitch from plucking string) Circular motion that causes same pitch

How Inharmonicity affect piano tuning?

You are tuning higher strings to the overtones of the first string If the notes an octave apart were tuned such that their fundamentals had a ratio of frequencies of 2, then the slightly raised second overtone of the lower note would beat with the fundamental of the upper note when played simultaneously. To avoid the beating, notes an octave apart are stretched, they are tuned to have a ratio of frequencies slightly greater than 2 Inharmonicity affects tone quality because they are excited at high overtones due to the sharpness of the hammer → affects sound → piano sounds more bright To produce uniform tone along the keyboard, the hammers must strike their respective strings at the same ratio along their lengths

Differences between sound production in piano and harpsichord

the sound production in a piano is done by the hammer striking the piano whereas the harpsichord is plucked to activate the strings. The piano has 7 octaves and the harpsichord only has 5. The harpsichords keys are thinner than a piano. A tone can be sustained in a piano, where it cannot be in a harpsichord. Lastly and most importantly, A piano player will have full control over the volume of sound produced; one can play soft and loud sounds. On the other hand, a harpsichord player does not have such control. The harpsichord is going to be overall more quieter.