Natural Frequency of Wires in Tension

Natural Frequency

• Any object will vibrate when struck, plucked, or strummed. For objects like wires or strings, the frequency of those vibrations is determined by the tension, length and mass of the wire. When the vibrations are strong enough, and when the frequency falls within the range of human hearing, these vibrations create an audible sound. The strings of musical instruments, like guitars or violins, are tuned to specific tensions to generate specific frequencies, or musical notes.

Tension

• The scientific formula for frequency in a wire is: Frequency = Speed/Wavelength. When a wire is clamped at both ends, its tension depends on how tightly the wire is pulled between the two endpoints. A wire's tension impacts its natural frequency by affecting the velocity, or speed, of the waves in the wire. If all other variables remain the same, increasing the tension in a wire causes the waves to move faster, resulting in a higher resonant frequency.

Mass

• While increasing or decreasing the tension in a wire can change the velocity of its waves, this speed is also dependent upon the mass of the wire. Two wires of identical length, strung at the same tension, have different natural frequencies if their masses are different. This is because it is more difficult to move a massive string compared to a less massive one, so the wave velocity in the more massive string is slower.

Length

• A string's length determines the wavelength of its natural frequency. The relationship between length and frequency is inverse, meaning that the smaller the length, the greater the natural frequency. If the mass and tension of two strings of different lengths are identical, the shorter string will vibrate at a higher frequency.