A string under tension has a fundamental frequency of 220 Hz. What is the fundamental frequency if the tension is doubled?

Key Concepts

Fundamental Frequency

The fundamental frequency is the lowest frequency at which a system oscillates. In the context of a string, it is determined by the string's length, tension, and mass per unit length. This frequency is crucial for understanding how musical notes are produced and perceived.

Tension in a String

Tension refers to the force applied along the length of a string, which affects its vibration characteristics. Increasing the tension in a string raises its fundamental frequency, as a tighter string vibrates faster. This relationship is essential for analyzing how changes in tension influence sound production.

Relationship Between Tension and Frequency

The relationship between tension and frequency in a vibrating string is described by the formula f = (1/2L)√(T/μ), where f is the frequency, L is the length of the string, T is the tension, and μ is the mass per unit length. Doubling the tension results in an increase in frequency, specifically by a factor of √2, illustrating how tension directly impacts the pitch of the sound produced.