Skip to main content
Physics LibreTexts

4.1: Introduction

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    A tensioned string is a classic example of controlled vibration which may create waveforms with many overtones or harmonics. This may result in a waveform considerably more complex in appearance than a simple sine wave although it will have a discernable period. Pythagoras studied the variables in the system circa 500 BCE and made important contributions to the science behind Western musical scales. The frequency of oscillation of a tensioned string is

    \[f = \frac{1}{2l} \sqrt{\frac{T}{u}}\nonumber\]

    where \(f\) is the frequency in hertz, \(T\) is the tension in kilogram meters per second squared (newtons), u is the mass per unit length of the string in kilograms per meter, and l is the vibrating length of the string in meters. In this experiment, the tension, \(T\), is simply the product of a suspended mass (kilograms) times the acceleration due to gravity (9.8 meters per second squared). That is, tension is a force and force is equal to mass times acceleration. Note that longer strings and more massive strings produce a lower frequency of oscillation and that increased tension increases frequency.

    This page titled 4.1: Introduction is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James M. Fiore via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?