Editing Cello (section)

==Physics==

===Physical aspects===
When a string is bowed or plucked, it vibrates and moves the air around it, producing sound waves. Because the string is quite thin, not much air is moved by the string itself, and consequently, if the string was not mounted on a hollow body, the sound would be weak. In acoustic stringed instruments such as the cello, this lack of volume is solved by mounting the vibrating string on a larger hollow wooden body. The vibrations are transmitted to the larger body, which can move more air and produce a louder sound. Different designs of the instrument produce variations in the instrument's vibrational patterns and thus change the character of the sound produced.<ref>{{cite book|last=Cowling|first=Elizabeth|title=The cello|url=https://books.google.com/books?id=46gXAQAAIAAJ|year=1983|publisher=C. Scribner's Sons|isbn=978-0-684-17870-7}}</ref> A string's fundamental pitch can be adjusted by changing its stiffness, which depends on tension and length. Tightening a string stiffens it by increasing both the outward forces along its length and the net forces it experiences during a distortion.<ref name="Bloomfield, Louis A 2001. pp 241-244">{{cite book|last=Bloomfield|first=Louis|title=How things work: the physics of everyday life|url=https://books.google.com/books?id=tgUvAQAAIAAJ|year=2001|publisher=Wiley|isbn=978-0-471-38151-8}}</ref> A cello can be tuned by adjusting the tension of its strings, by turning the tuning pegs mounted on its pegbox and tension adjusters (fine tuners) on the tailpiece.

A string's length also affects its fundamental pitch. Shortening a string stiffens it by increasing its curvature during a distortion and subjecting it to larger net forces. Shortening the string also reduces its mass, but does not alter the mass per unit length, and it is the latter ratio rather than the total mass which governs the frequency. The string vibrates in a standing wave whose speed of propagation is given by <math display="inline">\sqrt{\frac{T}{m}}</math>, where {{mvar|T}} is the tension and {{mvar|m}} is the mass per unit length; there is a node at either end of the vibrating length, and thus the vibrating length {{mvar|l}} is half a wavelength. Since the frequency of any wave is equal to the speed divided by the wavelength, we have <math display="inline">\mathrm{frequency} = \frac{1}{2l} \cdot \sqrt{\frac{T}{m}}</math>. (Some writers, including Muncaster (cited below), use the Greek letter {{mvar|μ}} in place of {{mvar|m}}.) Thus shortening a string increases the frequency, and thus the pitch. Because of this effect, you can raise and change the pitch of a string by pressing it against the fingerboard in the cello's neck and effectively shortening it.<ref>{{cite book|last=Muncaster|first=Roger|title=A-level Physics|url=https://books.google.com/books?id=Knov8XAyf2cC|year=1993|publisher=Nelson Thornes|isbn=978-0-7487-1584-8}}</ref> Likewise strings with less mass per unit length, if under the same tension, will have a higher frequency and thus higher pitch than more massive strings. This is a prime reason the different strings on all string instruments have different fundamental pitches, with the lightest strings having the highest pitches.

[[File:Spectrogram Cello D Arpeggio.png|thumb|upright=0.45|[[Spectrogram]] of a D chord arpeggiated on the cello. Yellow bands at the same level indicate the same harmonics excited by the bowing of different notes. Notes played from left to right: D–F{{music|#}}–A–F{{music|#}}–D.]]

A played note of E or F{{sharp}} has a frequency that is often very close to the natural resonating frequency of the body of the instrument, and if the problem is not addressed this can set the body into near resonance. This may cause an unpleasant sudden amplification of this pitch, and additionally a loud beating sound results from the interference produced between these nearby frequencies; this is known as the "[[wolf tone]]" because it is an unpleasant growling sound. The wood resonance appears to be split into two frequencies by the driving force of the sounding string. These two periodic resonances beat with each other. This wolf tone must be eliminated or significantly reduced for the cello to play the nearby notes with a pleasant tone. This can be accomplished by modifying the cello front plate, attaching a wolf eliminator (a metal cylinder or a rubber cylinder encased in metal), or moving the soundpost.<ref name="Berg, Richard E 2005. pp 314, 329">{{cite book|last1=Berg|first1=Richard E.|last2=Stork|first2=David G.|title=The Physics of Sound|url=https://books.google.com/books?id=4FpgQgAACAAJ|year=2005|publisher=Pearson Prentice Hall|isbn=978-0-13-145789-8}}</ref>

When a string is bowed or plucked to produce a note, the fundamental note is accompanied by higher frequency overtones. Each sound has a particular recipe of frequencies that combine to make the total sound.<ref>{{cite book|last=Chattopadhyay|first=D.|title=Elements of Physics|url=https://books.google.com/books?id=eA7g3aXePRoC|date=January 1, 2004|publisher=New Age International|isbn=978-81-224-1538-4}}</ref>