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Sound waves follow a certain mathematical function that is based on what is called the "sine" in trigonometry. The attached article may be way too complicated to read through, but you can see what a sine wave looks like, and start to get an idea how a wave graph relates to something that is vibrating or oscillating.

When we first learn about sound waves we may think that sounds move through the air are following some kind of 'wavy' path; this is not the case. The wave that we draw on graph paper is a way for us to understand the layers of pressure that move toward us. Sound really moves more like countless expanding bubbles nestled inside one another, starting from the source. The bubbles are fronts of slightly higher pressure, followed by 'troughs' of slightly lower pressure.

Looking at a graphed sine wave, time is measured along the bottom, going toward the right. The up and down positions at any moment tell you what the relative pressure (air pressure, if you are considering sound moving through air) is.

The higher the frequency of waves (the more tightly packed the waves are-- the more peaks there are, say, in one second of time) the higher will be the pitch you hear. The farther up and down the peaks and troughs are, the louder the sound will be.

2nd Answer:

A sound that that produces sinusoidal displacement of air molecules with respect to time is a pure tone. That means it is a steady note with no overtones.

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