Sound and Acoustic

Sound and acoustics

It is common to think that acoustics is the study of music. Although acoustics does comprise the study of musical instruments, it also includes an extensive range of topics, including: SONAR systems, noise control, ultrasounds for medical imaging and other processes, electroacoustic communication, seismology, etc. [1] In general, acoustics is the study of mechanical waves including sound, vibration, infrasound and ultrasound.

When talking about the acoustics, it is essential to answer the question: What is sound? It is nothing more than an acoustic wave produced when an object vibrates and communicates its motion to the surrounding medium. However, mechanical vibration does not have to cause the sound wave, due to the fact that a sound wave requires a medium that can be vibrated. Therefore, there is no transmission of sound in the vacuum. What is more, there are two types of sound waves: transverse and longitudinal. For transverse waves the displacement of the medium is perpendicular to the direction of propagation of the wave. Opposite to solid media, such as wood, iron or brick, liquids and gases are not able to transmit transverse forces. That is why, in this case, sound waves are always longitudinal waves, which means that the particles move in the direction of propagation of the wave. [2] And since this thesis deals only with propagation of sound in liquid and gaseous media, I will focus only on longitudinal waves, which are composed of compressions, where the parts of the medium closer together than normal, and rarefactions, where the parts of the medium are farther apart than normal. [3]

Sound parameters

Every acoustic wave is characterized by several parameters. The first one is frequency (f), which is the number of pressure variation cycles in the medium per unit time, or simply, the number of cycles per second. [4] The unit of frequency is Hertz [Hz]. The frequency range over which sound can be heard by the human ear is limited to the range of about 20 Hz to 20 kHz. Longitudinal mechanical waves below 20 Hz are called infrasound and above 20 kHz, ultrasound. Waves with the frequency below 400 Hz are considered to be low, waves in the range from 400 Hz to 3 kHz as an average and those at frequencies above 3 kHz are considered high.

Second very important parameter is wavelength (λ), which is the distance travelled by the wave during one cycle. It is given by the equation: , where v is a speed of sound in the specific medium and f is aforementioned frequency of the wave.

A sound wave is also characterized by a sound pressure (p), which is the local pressure aberration from the ambient atmospheric pressure caused by a sound wave. It is measured in pascals [Pa]. There is also a sound level (SPL) expressed in decibels [dB] and it is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is given by the equation: , where is the reference pressure.

Another essential parameter of an acoustic wave is sound intensity (I), which is the measure of the energy of an acoustic wave. Its unit is [W/m2]. It is equal to the mean value of the acoustic energy flux flowing during the time of 1 second by a unit area (1m2) oriented perpendicular to the direction of wave propagation. This value is rather difficult to measure. Therefore it is usually expressed in terms of sound pressure: , where p is a sound pressure, v is a speed of sound and is a density of the medium. Obviously, the sound intensity is proportional to the square of the sound pressure. When talking about the sound intensity, it is important to mention about the sound intensity level, which is used very often. It is a logarithmic measure of the sound intensity in comparison to a reference level. It is given by the equation [5]: [dB].

Basic concepts of sound

Besides the parameters of the sound, there are also a few concepts related to this topic, which are essential in sound analysis. One of them is tone, which is the sound that can be recognized by its regularity of vibration. A simple tone has only one frequency, although its intensity may vary. A complex tone consists of two or more simple tones, called overtones. [6] By using Fourier transform every sound can be represented as a graph of the harmonic spectrum. The most significant influence on the reception of sound has basic tone, which is the greatest common divisor of the component tones.
When talking about the sound analysis it is also crucial to mention about the noise. In general, noise refers to any unwanted sound. However, in relation to acoustics, noise is a group of sounds that has the continuous spectrum. A special kind of noise is called a white noise, which is the noise in which all the component frequency have the same amplitude. As it will be presented in further sections, the concept of noise is essential as far as this paper is concerned.
Another very important phenomenon is rumble. It refers to a low frequency sound from the bearings inside a turntable. It is based on the fact that during the generation of two sounds of similar frequencies one may hear the sound of the frequency of the difference of these two. Due to this fact, it is easy to generate the sounds with low frequencies, for instance for 300 Hz and 335 Hz, one hears the sound of = 35 Hz.

Sound processing

When talking about the sound and acoustics, it is crucial to mention about the sound processing. It is an extremely important part of my thesis, which will be shown in later sections, when discussing the results of my project.
A signal can be considered from two different viewpoints: time domain and frequency domain. To put it simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. [7] Obviously, a frequency domain analysis gives a lot more possibilities to analyse signal properly. Fortunately, every signal can be easily converted from time domain into frequency domain using various transforms. The good example of such a transform is Fast Fourier Transform (FFT), which is an efficient algorithm for computing Discrete Fourier Transform (DFT). Below there are some examples of different waveforms with their accompanying FFTs.