Cello vibrations and how a violin bow works

03 March 2009

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Ingredients

First of all we have just plucking a single string to give you a feel for what is going on. The video is slowed down by a factor of 40, so this string is vibrating at about 64Hz.

Then we tried plucking all the strings at the same time. The strings are all tuned a fifth apart, this means that as they get higher their frequencies are 3/2 times higher. You can see them go in and out of phase.

In this next video only the lowest string is being bowed, but because it is tuned to the same note as the second string the vibrations set up in the cello cause the second string to move as well.

They are moving in opposite directions because whenever the lower string is at the bottom of its vibration it is being pulled upwards by the cello, this means that due to conservation of momentum the cello and the second string must be pulled  downwards. If the forces on the two strings are in opposite directions then they will move in opposite directions.

How the cello bow works.

This was the video I was most impressed by, it shows the cello bow moving across the string from bottom to top.

You can see that the string moves smoothly with the bow until it gets near the end of its motion, at which point it quickly jumps back again. This is because friction is normally greater when two objects are stationary compared to when they are moving past one another

This means that many things from a bag you are dragging across the floor to your fingernails as you drag them across a blackboard tend to stick and then slip repeatedly creating a vibration.

What I found especially interesting was the way that the string is moving in this sawtooth pattern. Which is  very different from the  smooth sine wave vibration of the fundamental mode, and the string keeps on moving like this even when you stop bowing. This must mean that the bow is driving a set of harmonics which make the string move in a sawtooth pattern.