Audio Concept Zoo

A collection of concepts on audio and digital signal processing.

Decibel

decibel (dB), unit for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds. One decibel (0.1 bel) equals 10 times the common logarithm of the power ratio. Expressed as a formula, the intensity of a sound in decibels is 10 log10 ($S_1/S_2$), where $S_1$ and $S_2$ are the intensity of the two sounds; i.e., doubling the intensity of a sound means an increase of a little more than 3 dB. In ordinary usage, specification of the intensity of a sound implies a comparison of the intensity of the sound with that of a sound just perceptible to the human ear. For example, a 60-dB, or 6-bel, sound, such as normal speech, is six powers of 10 (i.e., $10^6$, or 1,000,000) times more intense than a barely detectable sound, such as a faint whisper, of 1 dB. Decibels are also used more generally to express the logarithmic ratio of two magnitudes of any unit, such as two electric voltages or currents (or analogous acoustic quantities). In cases where the ratio is of a squared quantity, 1 dB equals 20 times the common logarithm of the ratio.

The term bel is derived from the name of Alexander Graham Bell, inventor of the telephone. The unit decibel is used because a one-decibel difference in loudness between two sounds is the smallest difference detectable by human hearing. — Source: https://www.britannica.com/science/decibel

See also: dB What is a decibel?

Sound Intensity ($\mathbf{I}$)

• Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
• The SI unit of intensity, which includes sound intensity, is the watt per square meter $W/m^2$
• Sound intensity is defined as $\mathbf{I}=p\mathbf{v}$ where $p$ is the sound pressure $\mathbf{v}$ is the particle velocity. $\mathbf{I}$ and $\mathbf{v}$ are vectors with direction and magnitude and $p$ is a scalar.
  • the direction of sound intensity is the average direction in which energy is flowing
• The average sound intensity during time $T$ is given by $⟨\mathbf{I}⟩=\frac{1}{T}{\int }_0^{T}p(t)\mathbf{v}(t)\mathrm{d}t$
• For a plane wave: $\mathrm{I}=2{\pi }^2{\nu }^2{\delta }^2\rho c$ where $\nu$ is frequency of sound, $\delta$ is the amplitude of the sound wave particle displacement, $\rho$ is density of medium in which sound is traveling, and $c$ is speed of sound.
• Sound intensity is not the same physical quantity as sound pressure.

Sound intensity Level (SIL)

• Sound intensity Level (SIL) or acoustic intensity level is the level (a logarithmic quantity) of the intensity of a sound relative to a reference value: $L_I=\frac{1}{2}\ln \left(\frac{I}{I_0}\right)\mathrm{Np}={\log }_{10}\left(\frac{I}{I_0}\right)\mathrm{B}=10{\log }_{10}\left(\frac{I}{I_0}\right)\mathrm{dB}$ where
  • $\mathbf{I}$ is the sound intensity;
  • ${\mathbf{I}}_0$ is the reference sound intensity;
  • $1\mathrm{Np}=1$ is the neper;
  • $1\mathrm{B}=\frac{1}{2}\ln (10)$ is the bel;
  • $1\mathrm{dB}=\frac{1}{20}\ln (10)$ is the decibel
• The commonly used reference sound intensity in air is $I_0=1\mathrm{pW}/{\mathrm{m}}^2$ being approximately the lowest sound intensity hearable by an undamaged human ear under room conditions.

Sound pressure

• Sound pressure (or acoustic pressure) is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave
• The SI unit of sound pressure is the pascal (Pa)

Acoustic Impedance

• Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system.
• The SI unit of acoustic impedance is the pascal-second per cubic metre ($Pa\cdot s/m^3$)
  • or in the MKS system the rayl per square metre (rayl/m2)
• …while the SI unit of specific acoustic impedance is the pascal-second per metre ($Pa\cdot s/m$)
  • or in the MKS system the rayl.
• There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electric current resulting from a voltage applied to the system.

Wavelength

• Wavelength is the spatial period of a periodic wave—the distance over which the wave’s shape repeats.
  • It is the distance between consecutive corresponding points of the same phase on the wave (such as two adjacent crests, troughs, or zero crossings).
• Wavelength is the inverse of spatial frequency.
• Wavelength is commonly designated by $\lambda$ (the Greek letter lambda).

Frequency

Hertz (Hz) measures a sound wave’s frequency. Hertz measures a sound wave’s cycles per second that pass a set point on the horizontal axis. (Remember, each process has one compression and one rarefaction.) The frequency sound waves are measured in hertz. Therefore, Hertz (Hz) indicates the number of cycles per second that pass a given location. For example, if, while speaking, your diaphragm vibrates at 900 Hz, your diaphragm generates 900 compressions (increased pressure) and 900 rarefactions (decreased pressure). Pitch is a function of how the brain interprets sound frequency. A higher pitch is the result of higher frequency; lower frequency translates as lower pitch.

Period

• Period is the time duration of one cycle of the sound wave.
• The period is the reciprocal of the frequency.

Amplitude

The amplitude (strength or level of sound pressure) by the height of the sound wave. It’s related to the relative volume of the sound. When the wave’s amplitude is significant — as from a loud sound — the wave is high. The reverse is also true; softer sounds produce waves with a smaller amplitude. Lower volume equates to lower decibel (dB) levels; a decibel measures sound intensity. Zero decibels equates to the quietest sounds a human ear can hear. Decibels increase by a factor of six. A normal speaking voice is 60 dB.

Sound pressure (p, SPL,LPA)

Particle velocity (v, SVL)

Particle displacement (δ)

Sound power (P, SWL, LWA)

Sound energy (W)

Sound energy density (w)

Sound exposure (E, SEL)

Acoustic impedance (Z)

Transmission loss (TL)

Pitch

Pitch is the perceived property of sounds that allows their ordering on a frequency-related scale making it possible to judge sounds as “higher” and “lower” in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.