How do string tension, thickness, and density affect the pitch of a stringed instrument?

The fundamental frequency of a stretched string is determined by its physical properties and the tension applied to it, as described by Mersenne’s laws. These relationships explain how the pitch of a stringed instrument is controlled:

• Tension: The fundamental frequency is directly proportional to the square root of the tension in the string. Increasing the tension raises the pitch, while decreasing it lowers the pitch.1
• Mass per unit length (Thickness/Density): The fundamental frequency is inversely proportional to the square root of the mass per unit length. A thicker or denser string has more mass per unit length, which results in a lower pitch compared to a thinner, lighter string under the same tension.1

Instrument makers use these principles to design instruments with a balanced range. For example, the lower-pitched strings on a guitar or violin are constructed with greater mass—often by winding heavy wire with additional thin wire—to achieve lower frequencies without requiring excessively long strings or dangerously low tension.1