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4: Musical instruments

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    Musical Instruments: Learning Objectives
    • Explain the connection between instrument size and the frequencies of sound produced.
    • Describe a standing wave. Define node and antinode.
    • Use a standing waves model to explain how string instruments control pitch
    • Use a standing waves model to explain how wind instruments control pitch
    • Use standing wave model to explain the presence of overtones in musical sounds
    • Use standing waves model to solve problems related to string instruments and wind instruments.
    • Explain the relationship between forced vibrations and resonance.
    • Describe relationship between resonance and standing waves.
    • Distinguish between resonant and non-resonant amplification
    • Describe a Helmholtz resonator and describe difference between Helmholtz resonator and air column.

    How do musical instruments work? How can they take a seemingly unmusical input- like a pluck, the buzz of a reed or the scratch of horsehair against a metal string- and turn the input into musical sound? Why are there families of instruments (like violins, violas, cellos and basses) that sound similar? Why do larger musical instruments make generally lower pitches? Why do musical instruments almost always produce several frequencies at once, rather than pure tone?

    This part of the book explores how musicians control the properties of simple systems like strings and columns of air to control the pitch of the sounds they produce. New concepts- natural frequency, standing waves and resonance- go a long way to explaining many of the questions in the previous paragraph. Two physical systems commonly used in musical instruments- strings and air columns- will be explored in detail.

    This chapter builds on the key relationship among frequency, wavelength and wave speed (\(v=f\lambda\), with wavelength playing the central role.

    • 4.1: Natural frequency
      This page covers forced vibration and resonance, explaining that objects vibrate from external forces and highlighting the significance of natural frequency, which determines a system's oscillation. It distinguishes natural frequencies from frequency response and illustrates resonance through examples such as musical instruments and sound dynamics.
    • 4.2: Vibrating strings
      This page explores the physics of stringed instruments, detailing how sound is produced through standing waves formed by stretched strings. It explains modes and their frequencies, particularly highlighting the fundamental and higher modes, with the fifth harmonic mode (n=5) exemplified at a wavelength of 28 cm and a frequency of 490 Hz.
    • 4.3: More about strings
      This page covers the anatomy and function of string instruments, highlighting components like strings, tuning pegs, and the fingerboard. It explains sound production through open strings and the effects of tuning adjustments on pitch. The page details how string thickness influences pitch and how fingering alters vibrating length.
    • 4.4: Vibrating air columns
      This page explains the sound production mechanism in wind instruments, focusing on how vibrating air columns in tubes create pitch influenced by length. It covers how different tube configurations exhibit unique standing wave patterns, impacting frequencies and resonant behavior.
    • 4.5: Helmholtz resonators
      This page explores resonance in wine bottles, introducing Helmholtz resonators, which differ from traditional air column models by considering the bottle's shape. It defines resonant frequency based on factors like air speed and bottle dimensions. Helmholtz resonators have practical applications in noise dampening in musical instruments, architectural acoustics, and engineering systems.
    • 4.6: Other resonators
      This page explores various resonating systems beyond basic strings and air columns, detailing types such as woodwinds, drums, and percussion. It contrasts harmonic systems, which produce harmonious overtones, with anharmonic systems that generate dissonant sounds. Examples include thin membranes and vibrating bars. Additionally, the page offers references for further investigation into specific instrument resonances, such as those found in metal bars and drum heads.
    • 4.7: Review and Homework- Standing waves and resonance
      This page covers fundamental concepts of vibrations, sound production, and resonance in musical instruments. It explains key terms such as forced vibrations, natural frequency, and standing waves, using examples from various instruments. The impact of string length, tension, and material on frequency and pitch is highlighted, supplemented by review questions for concept application and numerical problems for practical calculations related to sound behavior in instruments.

    Thumbnail: Close Up Of Guitar Tuning Pegs (Unsplash License; Grant Davies on Unsplash)

    This page titled 4: Musical instruments is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by David Abbott via source content that was edited to the style and standards of the LibreTexts platform.