Science Buddies: "Ask an Expert"

Hi experts,
I am currently doing an experiment on twanging different lengths of a steel ruler on a table. By pulling and releasing the overhanging end of the ruler, I have recorded the sounds and determined their frequencies. As expected, the frequency of the sound decreases with a longer portion of the ruler. I know that the density, length and possibly the thickness of the ruler affect the frequency of the sound produced, but is there an equation relating these variables together with respect to sound? My ultimate goal is to determine lengths of the steel ruler I have to pluck in order to make a particular frequency. Any help will be appreciated

Hi coconutwood,

You're definitely on the right track. The equation you're looking for exists, but I don't have it memorized and wouldn't want to give away the answer anyway . Here are a few additional definitions and terms you might want to look up. Searching for the right combination of these terms should allow you to find what you're looking for.

cantilever beam is the term for a beam that's fixed at one end and free at the other end, like what you've described with the ruler (as opposed to something like a bridge, that's fixed at both ends).
natural frequency and resonant frequency are two terms that are used interchangeably. As the name implies, this is the frequency at which an object will "naturally" vibrate when you pluck it, like you're doing with the ruler (this concept applies to all physical objects - a guitar string, a child on a swing, etc).
Young's modulus or elastic modulus is another physical property of the material that matters. It measures how "stiff" a material is (how hard the material is to stretch). Sometimes it's just called "stiffness." It is usually represented by a capital letter E in engineering equations (not to be confused with E for energy in some physics equations).
second moment of area, also called moment of inertia depending on where you look.This is a geometric property that depends on the cross-sectional shape and dimensions of the beam (for example, it's different for a circle and a rectangle). It's usually represented by a capital I (the letter "eye") in engineering equations. For a rectangle it will depend on the width and thickness of the cross-section.

Hope that helps! From some quick googling it looks like you should be able to find the equation you need online.