AVEM Classroom 06 - Frequency, Bands and Octaves

Frequency

Frequency is the number of wave cycles occuring in the period occuring in the period of a second—cycles per second. The standard unit for measuring cycles per second is the hertz (Hz). Figure 4-2 illustrates frequency.

  Although the sounds you hear every day are complex waveforms, every sound can be broken down to a series of individual simple sine waves at different frequencies. Fourier-analysis is the mathemical process used to calculate what is known as the Fourier series of component frequencies for a waveform. The calculation and mathematical manipulation of the components of a waveform's Fourier series lies at the heart of all digital signal processing (DSP) applications.

  Frequency and wavelength are related to each other by speed of transmission in a medium. In Figure 4-3 you can see the mathematical relationship between speed of transmi-ssion, wavelength, and frequency. Using these formulas you can calculate the wavelengths at the limits of the frequencies most humans can hear—20Hz to 20kHz.

     The wavelength at 20Hz = 343/20 = 17.2m (56.25ft)

     The wavelength at 20kHz = 343/20,000 = 17.2mm (0.67in)

  As you can see from these formulas, wavelength and frequency are inversly proportional, which means that the lowest frequencies have the longest wavelengths, and the highest frequencies have the shortest wavelengths.

Figure 4-2  Frequency is the number of cycles per second         

Figure 4-3  The relationship betweem frequency, wavelength, and velocity

Figure 4-2:How do I calculate the period of a 60-cycle AC sine wave?.Luciana Zoso.2018                                                                                                                                      Figure 4-3:Quizziz. Speed of Wave

v = velocity of wave in medium (m/s)

f = frequency of wave (Hz)

v = λ*f     velocity = wavelength x frequency

Bands and Octaves

The spectrum of frequencies we can hear is often divided up into bands based on the doubling of frequencies between bands. The name given for these bands are octaves, a mu-sical term based on the Western European musical scale, in which each band is divided into eight tones. Octaves comes from octavus, the Latin word for eight.

   Frequencies are divided up in bands this way because the human ear's response to frequency is logarithmic. To our ears each doubling (or halving) of a frequency sounds like a similar interval. The interval between a tone at 220Hz and one at 440Hz sounds the same as the interval between a tone at 440Hz and one at 880Hz, even though each interval is a doubling of frequency.

   In Table 4-1, the intervals between 500Hz, 1kHz, 2kHz and 4 kHz all sound identical to our ears, despite the bandwidth between them being substantially different.

   In general audio apllications, the spectrum of human hearing—20Hz to 20kHz—is divided into 10 bands, each one octave wide. Each band is usually identified by its center freq-uency. For some purposes, such as in graphic equalizers, the spectrum may be further subdivided into 1/3 octave bands.

Source:CTS Certified Technology Specialist Exam Guide.Chapter 4 Audio Systems. pg 37-38