There are many different ways to create vibrations, but the most common method is to use a string, a membrane, or a column of air. When a string is plucked, it vibrates at its natural frequency, which is determined by its length, tension, and mass. The same is true for a membrane, such as a drumhead, and a column of air, such as in a wind instrument.
The pitch of a sound can also be affected by the shape of the object that is vibrating. For example, a guitar string that is plucked near the middle will produce a higher pitch than a string that is plucked near the end. This is because the string is shorter near the middle, so it vibrates faster.
The pitch of a sound can also be affected by the materials that are used to make the instrument. For example, a guitar made of wood will produce a different sound than a guitar made of metal. This is because the different materials have different densities and stiffnesses, which affect the way that they vibrate.
By combining different materials, shapes, and sizes of strings, membranes, and columns of air, musical instruments can produce a wide variety of sounds at different pitches.