I am a violinist, and I wonder why there is harmonics in a string. When I
place my finger somewhere near the center of the string, the pitch produced is an octave
higher than the string.
This is probably going to be a long reply. I hope all this makes sense. I am a music teacher,
physics teacher, and student of the violin, so I think we can talk.
When you bow the violin, you set the string vibrating. Vibrations are what our ears hear.
The different pitches are caused by the frequency of the vibration, in other words, how often
it is vibrating per second. Frequency is measured in hertz, which means, cycles per second. An
orchestra will tune to an A of 440 Hz. You might have seen a tuning fork with a note and
frequency marked on it. We also have electronic tuners to tune to.
Now what you are describing is called harmonics. A tuning fork vibrates with a pure tone. It's
"clean". There are no overtones. (A tuning fork is also handy, portable, and easy to tune to.)
Any other instrument vibrates with what are called overtones. The entire string length is set
into vibration by the bow; from bridge to nut. Let us say it is your A string. That is called
the fundamental pitch. You cannot go lower, (well technically you can if you loosen the string,
but let us not do that right now.) The speed of sound is constant in your string, no faster, no
slower, just one speed. The equation for the relationship between the speed of sound the
frequency and the wavelength goes like this: Velocity = Frequency X Wavelength If you know a
little math and we keep the Velocity side constant, if wavelength gets smaller, frequency has
to get bigger. Frequency determines pitch. The higher the frequency, (bigger number) the
higher the pitch.
So back to the violin string. To play an A# on the string, you put your finger down on the
string. This makes the string shorter, (smaller wavelength), so pitch goes up. When you put
your finger exactly halfway down on the string, you've made the wave length, (string length)
half as big but this doubles the frequency. If you double A 440, you get the next A 880. If
you can put your finger about 1/4 of the way from the tailpiece, you might be able to squeak
out the next octave. It is all multiples of the frequencies. Who would have thought math and
music could fit together so beautifully?
Take physics in high school and hopefully you will learn a little more about the other
instruments and how all the sounds are produced.
Look in your library for some Physics books. I was looking for something to recommend, but all
I can come up with are textbooks. If your school has a copy of Holt Physics, they do a pretty
decent job of explaining this in the chapter on sound.
I hope this answers your question. E-mail me back if you need a better explanation. I will try
my best. Have fun with your violin full of Physics!
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Update: June 2012