Did you know that sounds can be described mathematically? We can draw graphs that represent the volume (how loud or quiet a sound is) and the pitch (how high or low the sound is). More importantly, when we understand the pattern of these sounds, we know how to achieve these desired sounds when making instruments.
Here are two examples of sound waves:
What do we notice about these waves? The louder ones are taller compared to the soft waves. That is, they have a higher amplitude (height of the wave). The higher the amplitude of a sound wave is, the louder it is.
However, we also notice that both sets of these waves have cycles that are about the same width. (A cycle is equal to a single wavelength, which is the distance from one point on one single wave to the same point on the next adjacent wave.)
So what happens if we change the width of a wave cycle?
The skinnier the waves get, the more of them we can fit together in the same amount of time. This is higher frequency: the waves cycle more frequently in a given time frame. A higher frequency means that our ears hear a higher pitch, like a whistle. A lower frequency means that we hear a lower sound, like a bass drum.
How quickly an object vibrates determines the pitch that our ears hear. Think of a guitar, which has 6 strings, all different sizes. Imagine that you pluck the skinniest string, and you watch it vibrate as it plays a high note. Then you pluck the thickest string, which plays a much lower note. Why is that? Because the thickest string is just that - it's thicker, meaning there's more material to it (more mass); it cannot vibrate as fast as the skinniest string.
The frequency we hear from many types of instruments depends on how long or how thick parts of the instruments are. So how can we use this knowledge to create musical instruments?