The Mechanics of Hearing

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Learning Objectives

Be able to describe at least 3 uses of sound.

Understand what sound waves are (pressure changes).

Know the relationship between everyday sound waves and atmospheric pressure (unit in Pascal).

The physical phenomenon of sound is a disturbance of matter that is transmitted from its source outward. Hearing is the perception of sound, just as seeing is the perception of visible light. On the atomic scale, sound is a disturbance of atoms that is far more ordered than their thermal motions. In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. Thus, sound waves can induce oscillations and resonance effects.

For example, a speaker produces a sound wave by oscillating a cone, causing vibrations of air molecules. It vibrates at a constant frequency and amplitude, producing vibrations in the surrounding air molecules. As the speaker oscillates back and forth, it transfers energy to the air, mostly as thermal energy. But a small part of the speaker’s energy goes into compressing and expanding the surrounding air, creating slightly higher and lower local pressures. These compressions (high-pressure regions) and rarefactions (low-pressure regions) move out as longitudinal pressure waves having the same frequency as the speaker—they are the disturbance that is a sound wave. (Sound waves in air and most fluids are longitudinal, because fluids have almost no shear strength. In solids, sound waves can be both transverse and longitudinal.)

 

As a speaker vibrates to create sound the waves has points of high compression and low compression, call rarefaction. This image displays these ideas.
Figure 5.1.1. Sound pressure waves. (a) A vibrating cone of a speaker, moving in the positive x-direction, compresses the air in front of it and expands the air behind it. As the speaker oscillates, it creates another compression and rarefaction as those on the right move away from the speaker. After many vibrations, a series of compressions (high pressure, HP) and rarefactions (low pressure, LP) moves out from the speaker as a sound wave. The red graph shows the gauge pressure of the air versus the distance from the speaker. Pressures vary only slightly from atmospheric pressure for ordinary sounds. Note that gauge pressure is modeled with a sine function, where the crests of the function line up with the compressions and the troughs line up with the rarefactions. (b) Sound waves can also be modeled using the displacement of the air molecules. The blue graph shows the displacement of the air molecules versus the position from the speaker and is modeled with a cosine function. Notice that the displacement is zero for the molecules in their equilibrium position and are centered at the compressions and rarefactions. Compressions are formed when molecules on either side of the equilibrium molecules are displaced toward the equilibrium position. Rarefactions are formed when the molecules are displaced away from the equilibrium position. (Credit: Openstax. License: CC BY 4.0)

Sound waves are pressure changes, usually in air. Compression and rarefaction describe the regions of high and low pressure, respectively, that form when something vibrates and starts a sound wave. The pressure changes propagate (travel) at a rate of 340 m/s (1100 ft/s) in air; 1500 m/s in water.

This image shows how longitudinal waves squeeze molecules together as they approach and stretch them apart as they leave.
Fig.5.1.2. Sound Waves. Sound travels through the air and other matter as longitudinal waves (also called compression or pressure waves). These waves have points of compression and rarefaction which push the waveforms forward. (Credit: Christophe Dang Ngoc Chan. Provided by: Wikimedia Commons. License: CC-BY SA 3.0)

The Pascal is the standard unit for pressure (force per area); for reference atmospheric pressure (at sea level) is 101 kPa. An express subway train generates pressures of ~2 Pa, and conversational speech generates sound waves with intensities of approximately 20 millipascals (mPa). So the sounds we hear are tiny modulations of the air pressure.

Now how do we interpret these pressure waves? Our auditory system converts pressure waves into meaningful sounds. This translates into our ability to locate sounds in nature, to appreciate the beauty of music, and to communicate with one another through spoken language.

 

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OpenStax University Physics Volume 1 Section  17.1 Sound Waves
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 OpenStax, Psychology Chapter 5.2 Waves and Wavelengths
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Cheryl Olman PSY 3031 Detailed Outline
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Introduction to Sensation and Perception Copyright © 2022 by Students of PSY 3031 and Edited by Dr. Cheryl Olman is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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