Sound Amplitude

FIELDS OF STUDY: Acoustics; Classical Mechanics; Fluid Mechanics

ABSTRACT: The amplitude of sound waves determines their intensity; a large amplitude indicates an intense sound. Amplitude is measured by the displacement of the medium (such as air) through which sound waves travel. The sensory ability of the ear and brain limits the perceived loudness of sounds. Loudness and intensity are measured using decibels (dB), which relate sound intensity to human hearing on a logarithmic scale.

PRINCIPAL TERMS

• decibel: abbreviated dB; a unit of measure that quantifies sound intensity in relation to human hearing. It follows a logarithmic scale starting at zero for near silence.
• displacement: the distance particles in a medium are moved from their equilibrium by a wave; used to determine amplitude.
• frequency: how often a complete wave cycle occurs, directly proportional to the energy content of a wave and inversely proportional to wavelength; measured in hertz (Hz).
• intensity: in acoustics, sound power per unit area; measured in decibels or watts per square meter.
• loudness: the perceived intensity of sound; the objective intensity of sound in individual variations in hearing ability.
• noise: in acoustics, any sound whether wanted or not; may also describe background sound that obscures a desired signal or sound.
• perception of sound: the ability to perceive mechanical waves in one’s environment (e.g., air, water) as sounds, limited by the physiology of the ear and the brain’s ability to interpret information from sound waves.
• pulse: a lone disturbance passing through a medium from one place to another, similar to a wave but not cyclical and repeating.
• wavelength: the distance between crests of a wave; all electromagnetic radiation is transmitted as waves, with longer wavelengths corresponding to lower frequencies and less energy and vice versa.

The Three Wave Properties

Amplitude is one of the three major properties used to describe all waves, along with wavelength and frequency. These properties apply whether dealing with mechanical waves, such as sound waves, passing through a medium such as air or water, or electromagnetic waves, such as light and heat, passing through empty space. In mechanical (sound) waves, amplitude is determined by how much a wave displaces the medium it is traveling through.

Sound forms compression (longitudinal) waves, and the motion of the wave is parallel to the direction that energy is being transferred. Rather than up-and-down or side-to-side movement, compression waves travel as repeated, cyclical pulses of compression and rarefaction (expansion) in their medium. Amplitude in compression waves is measured as the maximum displacement of the particles of the medium from their normal resting state. Sound traveling through air is measured by air pressure at various points along the wave.

Amplitude and Irregular Pulses

A sound wave is cyclical and has a regular pattern of displacement. If something other than a regular pattern of displacement produces sound, such as with the vibration of a guitar string, the individual bursts of sound are considered pulses. A pulse can be thought of as a lone burst of disturbance. Calculating the amplitude of sound being generated as a series of irregular pulses offers unique challenges. In these situations, sound amplitude may vary from pulse to pulse, and attempts to measure amplitude hinge on determining what to base the measurement on. Choices include the average value of amplitude over time, the instantaneous amplitude, or the peak amplitude.

Amplitude, Loudness, and Intensity

In fundamental terms, amplitude reflects how much energy a wave is carrying. Large amounts of energy allow the wave to displace its medium farther. Wavelength and frequency, which are inversely related, also reflect a wave’s ability to transfer energy over time. Assuming equal amplitude, a long-wavelength, low-frequency wave will deliver less energy over time than a short-wavelength, high-frequency wave.

The amplitude and energy content of a sound wave is interpreted as loudness by the human ear. Intensity describes the sound power per unit area at a given point, regardless of a person’s ability to hear. Humans perceive the amplitude of sound as loudness only when our ears and brains can pick up and successfully interpret the sound waves. Even if a person is unable to hear certain sounds, sounds of sufficient intensity can be felt as vibrations by the rest of the body, as when standing near a sound system at a concert.

Frequency, in the form of wavelengths, forms the other half of the human perception of sound. Pitch, whether a sound is "high" or "low," corresponds to frequency. High-frequency sounds are associated with high pitches, and low-frequency sounds, low pitches.

Quantifying Loudness

Amplitude for all waves is measured using units of distance, such as meters, but the intensity and loudness of sound are quantified using the decibel (dB). Decibels measure intensity and loudness on a logarithmic scale. Its baseline value of zero is set at what a typical human would perceive as near-total silence. A sampling of typical sounds and their decibel values include:

• silence: 0 dB
• whisper: 20 dB
• public library: 40 dB
• dishwasher: 80 dB
• thunder: 120 dB

Exposure to intense sounds can cause a variety of problems. The threshold for annoying noise is usually somewhere between 70 to 80 dB, with discomfort increasing along with intensity. Any sound at 80 dB or higher can cause hearing damage with long-term exposure. At 110 dB, average humans will begin to experience physical pain from the sound.

Physical Effects of High-Intensity Sound

Sound waves of a high enough intensity can carry sufficient energy to influence their environment in other ways than producing sound. Sounds of sufficient intensity, for instance, can damage the sensitive organs of the ear. High-intensity ultrasound (very high frequency sound) can be a benefit too. It is often used therapeutically to penetrate organ tissues, and narrow, high-intensity pulses of sound are capable of breaking up kidney stones with minimal damage to surrounding tissue. On the other hand, sufficiently high intensity sound can cause unwanted tissue damage—up to and including the total rupture of an eardrum membrane at intensities of 150 dB and above. Standing within twenty-five meters of a jet taking off or near firecrackers or shot-gun blast will produce sound at 150 dB or above.

Sound Amplitude in Everyday Life

Coupled with frequency, amplitude enables musicians and engineers to accurately describe everything from the twang of a guitar to the thump of a bass drum. For physicists, amplitude provides valuable information about the energy content of a sound wave. Understanding the relationship between sound amplitude, intensity, loudness, and potential hearing damage enables engineers to design devices that produce sounds that are safe or devices that can help protect human ears in otherwise dangerous sound environments. Measurements of amplitude and frequency enable biologists to describe the songs of birds and note how they change over time due to evolution. The amplitude of sound waves is an important quantification of what humans commonly perceive as loudness of sounds.

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