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# Fundamentals of Acoustics: Introduction to Sound

By Marshall Williams 14 January 2021

Acoustics is the science of sound and a branch of physics. The scope of acoustics is not limited to phenomena that can be heard by humans and animals, it also includes phenomena with frequencies so low (infrasound) or so high (ultrasound) that cannot be heard by a normal person. These are also considered sound.

Sound is a vibration that propagates as an acoustic wave, through an elastic transmission medium such as a gas, liquid. Sound propagates in the form of longitudinal waves, involving a succession of compressions or rarefactions in the elastic medium.

Amplitude

The amplitude of a sound wave is the measure of the height of the wave. The amplitude of a sound wave can be defined as the loudness or the amount of maximum displacement of vibrating particles of the medium from their mean position when the sound is produced. It is the distance between crest or trough and the mean position of the wave.

Figure 1. Amplitude of a sinusodial wave

Frequency

Before we speak about the frequency, we will first discuss the period of sound. A period can be said to be the time taken to do something. If an event occurs repeatedly then the event is said to be periodic. The time taken by the periodic event to repeat itself is known as the period. The time taken by the particle to complete one vibration cycle is the time period for that particle.

Period= 1/Frequency

The period is the reciprocal to the frequency. The frequency of sound, also known as the frequency of oscillation, is the number of oscillations per second. It is measured in hertz (Hz). The frequency of a wave, in general, means how frequently the particles of a medium vibrate when a wave moves through the elastic medium.

Frequency= 1/Period

Figure 2. Period of a sinusodial wave

Wavelength

The wavelength (λ), is one of the more straightforward acoustic concepts to imagine. Simply, it is the size of a wave measured from one peak to the next.

= speed of soundfrequency

The wavelength of a sound is inversely proportional to it’s frequency. In other words, the higher the frequency, the shorter the wavelength.

Figure 3. Wavelength in air versus frequency under normal conditions

Velocity

The propagation speed, or acoustic velocity, of acoustic waves is a function of the medium of propagation. In general, the acoustic velocity (c) is given by the equation:

c= C

Where C is a coefficient of stiffness (the bulk modulus) and is the density in kg/m3. Thus, the acoustic velocity increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the materialand decreases with the density.

Decibels

The basic unit of level in acoustics is the decibel (dB). In acoustics, the term “level” is used to designate that the quantity is referred to some reference value.

The decibel, as used in acoustics, is a unit expressing the ratio of two quantities that are proportional to power. The decibel level is equal to 10 times the common logarithm of the power ratio:

dB=10logP1P2

In this equation P2 is the absolute value of the power under evaluation and P1 is an absolute value of a power reference quantity with the same units. If the power P1 is the accepted reference value, the decibels are normalized to that reference value. In acoustics, the decibel is used to quantify sound pressure levels that people hear, sound power levels radiated by sound sources, the sound transmission and more. Decibels are always related to logarithms to the base 10, so the notation 10 is usually omitted. The decibel is a dimensionless quantity. Therefore, when using decibel levels, reference needs to be made to the quantity under reference level.

Loudness

Loudness, in acoustics, is the attribute of sound that determines the intensity of auditory sensation produced. The loudness of sound as perceived by human ears is roughly proportional to the logarithm of sound intensity: when the intensity is very small, the sound is not audible; when it is too great it is dangerous and painful to the ear. The sound intensity that the ear can tolerate is approximately 1012 times greater than the amount that is just perceptible. This range varies from person to person and with the frequency of sound.

In conclusion, the terms described here are the most fundamental in acoustics. This is the first part in a blog series about the fundamentals of acoustics. Next time we will cover the propagation of sound.