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What is the logic behind this ?

As the larger instruments have larger gaps between the strings, I would have expected a larger bow to accomodate more easily continuous bowing while changing strings.

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I am reminded of the old joke about the relative sizes of violas and violins. –  bmargulies Apr 27 '11 at 2:16
    
@bmargulies: we are in beta and I am accustomed to hearing viola bashing. Please entertain us if it is relatively Safe For Work. –  ogerard Apr 27 '11 at 15:50
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Q: Why are violas bigger than violins? A: They aren't. The violinists heads are bigger. –  bmargulies Apr 27 '11 at 17:01

3 Answers 3

up vote 40 down vote accepted

It actually has to do with the physics of sound production for the bowed string instruments.

The sound is produced on the viol family of instruments by the string "slipping across" the bow. That is, the bow catches (by friction) the string, displaces it a certain distance, until the restorative force from the tension in the string overcomes the friction and snaps back to original position (here using the common fact that static friction is stronger than dynamic friction, so once the string starts moving, it will essentially return to starting position before being caught by the bow again).

Now, the pitch produced by the string is given by the frequency of the string vibration. For higher pitched instruments the frequency is higher: the string must vibrate faster. To build up resonance, you must pull the bow at the same speed as the vibration speed of the string (else you may set up destructive interference making the bowing ineffective). To attain this faster vibration, the bow needs to displace the string at a higher rate.

Therefore the typical bowing speed is higher for higher pitched string instruments.

Because you bow faster on a violin, to hold the note for the same length of time without returning the bow requires a longer bow than on, say, the cello. This is why the higher pitched string instruments have longer bows. (Note that the viola bow is only marginally shorter than the violin one; the two instruments have three strings in common.)

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There is, of course, a different reason for the length of bows of non-full-size instruments: you give shorter bows to kids with shorter arms so they can build up good bowing habit. A 10 year old with a 75 cm bow will never be able to pull far enough to get close to the tip. –  Willie Wong Apr 27 '11 at 0:55
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Excellent answer! I never would have guessed that there was so much physics behind this simple question. –  Ben Alpert Apr 27 '11 at 1:52
    
I have accepted this very nice answer. It is a pity I could not accept Gauthier's as well as they complement each other. –  ogerard Apr 27 '11 at 16:59
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it also explains partly while playing arpeggios is so tricky : you need to adapt the bow speed quickly between strings as you cross them. –  ogerard May 2 '11 at 16:10

It ain't necessarily so... I have two bass bows, the shorter of which is about the same length as my cello bow...

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Have you any comments about the difference you experience between the two bows? Have you already tried to cross (the cello bow on the bass and reverse)? –  ogerard May 9 '11 at 17:24
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The differences? the feel of the bow in the hand, the balance - it's all personal stuff. What's not so personal is that the tone produced by each bow is different - the longer bow is more of a solo / chamber bow - good tone, very easy to use. the shorter one (which was more expensive) seems to give more volume, but a slightly edgier tone, and I generally only use it for more modern orchestral stuff. –  Thomas Rushton May 10 '11 at 16:17
    
Can you include the names and eventually a picture comparing them? :) –  Tom Wijsman May 12 '11 at 15:17

Beside Willie Wong's nice answer, a double-bass player needs more pressure on the bow than a violin player. The longer the distance between your hand and the tip of the bow, the greater the force your wrist would need to apply.

In other words, playing the double-bass with a bow as long as a violin's may require too much wrist strength for playing with the tip of the bow.

Another aspect: the bow is also wider for larger instruments (more strength is needed to get the thicker strings to vibrate). A wider bow would easily get too heavy if it had the same length as the narrower ones.

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Ah yes, I forgot about this part. To produce a "smooth" sound on the lower pitch instruments also requires the bow to be heavier (so as to have larger angular momentum and less likely to be "bounced" away by the string). This puts further physical constraints to what Gauthier described. –  Willie Wong Apr 27 '11 at 12:43
    
+1 for this important complement to Willie's. –  ogerard Apr 27 '11 at 17:00
    
Having played double bass, this answer makes perfect sense. It's a question I'd thought about before but could never answer. –  Michael May 3 '11 at 22:40
    
Also, bass rosin is infinitely more sticky than violin or cello rosin. Once we get the string vibrating, we can sustain a long, quiet note while moving the bow extremely slowly and still getting a lot of resonance. A violin doing the same thing would have to change bow directions more often than a bassist, otherwise he would get a low-quality sound. –  Lotus Notes Jun 1 '11 at 22:30

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