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I'm trying to build my own string instrument. I can make the string however long I want it to be, the instrument should play a B which is at 493.9Hz. What calculations do I need to do?

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1) There are an infinite number of (theoretical) solutions to this based on changing the length ($L$), the mass ($m$), and the tension ($T$) of the string. You can attempt to find an approximate solution based on the materials you want to use.

$$f = \frac{\sqrt{\frac{T}{m/L}}}{2L}$$ http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html

2) Real instruments can't hold tension precisely over time, and other parts of the system (like the frequency response of materials in the body) can change as well. To be useful, some mechanism for changing the parameters (usually the tension) is necessary. Then you can tune it to the specific frequency you want as conditions change.

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