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6 Sound andAcoustics: AnOverview
107
threshold measures do not reveal any problems, tests of hearing (such as speech discrimination and intelligibility) performed in noisy environments do [4].
Experiments on animals have demonstrated that prolonged exposure to moderate acoustic noise (~100dB for around 2h) can cause TTS and HHL [9]. The features and connection between HHL and acoustic noise exposure in humans are still being determined, and there are currently a lot of contradictory data [4].
6.3 Acoustic Properties ofSound
When we hear, our ear canals take in vibrations from the surrounding environment and translate them into nerve impulses that travel to our brain, where they are pro­cessed as audible sounds. Sounds are created when an object that vibrates, like a guitar string being plucked, causes pressure pulses of air molecules that vibrate, called sound waves. The ear detects and analyzes many physical properties of the waves to differentiate between subjective features of a sound, such as its volume and pitch. The perceived frequency of sound waves, or pitch, is the number of wave­lengths passing a xed place in one unit of time. The unit of measurement for fre­quency is hertz, which stands for cycles per second. While the human ear is most acute and capable of picking up sounds in the 1000–4000Hz range, the full spec­trum of audible sounds spans roughly 20–20,000Hz, at least for typically develop­ing juvenile ears. While other mammals can hear them, sound waves with an even higher frequency are called ultrasonic. The sense of the strength of sound, or the pressure that sound waves impose on the tympanic membrane, is what we mean when we talk about loudness. A sound’s force, intensity, and, by extension, volume are all proportional to its amplitude or strength. One way to convey the relative amplitude of a sound on a logarithmic scale is via its measurement in decibels (dB), commonly used to report sound intensity. Decibels are a measure of good intensity relative to one another and a reference sound audible to the average person at a fre­quency within the audible range. A human ear can detect sounds at around 130dB, the threshold at which they start to feel discomfort, and at 0 dB, the threshold at which they are nearly inaudible [10].
6.3.1 What Is Sound?
A combination of vibrations from a sound source or sources and the waves that travel through the air to reach the ear is what we call sound. When a sound source regularly vibrates back and forth, it creates the most basic sound wave: a sine wave. Among the many characteristics of a sine wave are its frequency and amplitude [2].
The following picture shows a tuning fork producing a sine wave. The wave begins at a neutral point, travels to an extreme position, turns about, travels back to the neutral point, achieves its maximum at the other extreme, and, nally, returns to the neutral point. As long as the tuning fork is vibrating, this vibration pattern— called a cycle—will continue to recur. A wave’s period is the time it takes for one
108
Decibel level noise level dividedbyreference level=(10 10log
))
.
cycle to nish. The number of times a wave’s cycle completes in 1 s is called its frequency, measured in hertz (Hz). How far a wave travels from its neutral point to its maximum displacement position is its amplitude [2].
The practical ramications of these wave properties are signicant. A wave’s amplitude is proportional to its loudness or intensity, whereas its frequency is what we hear as pitch. Complex sine waves of varying frequencies and intensities make up most of the sounds we hear. A mathematical description of these intricate sounds could be found in a Fourier transformation. This method simplies audio by sepa­rating it into its component sine waves. When exposed to auditory stimuli, the ear also conducts this analysis [2].
N. Sarı et al.
6.3.2 Sound Intensity
Research into human hearing typically centers on determining the lowest audible volume. This is the auditory threshold. Although such measures are commonplace in clinical and fundamental research settings, they are complicated due to the broad frequency spectrum that the human ear can perceive. So, to make the units of mea­surement more manageable, the eld of hearing science employs a sound intensity measurement. The decibel (dB) used in this intensity scale is dened as follows [2]:
Sound pressure divided by reference pressure equals 20 log10in decibels.
The following features of the decibel scale can be noted [2]:
It is a relative scale based on a ratio that compares sound pressure or intensity with a specied reference level. The reference level is 20uPa (2×105N/m2), the lowest sound pressure most people can hear. Therefore, the intensity level in deci­bels equals 20 log10 (sound pressure/20uPa) [2].
This scale is logarithmic not linear. Doubling sound pressure results in a “6-dB increase in measured sound pressure”, while a “10-fold change in sound pressure” is reected by a “20-dB change in measured sound pressure” [2].
The logarithm of 1 equals 0. Accordingly, 0-dB SPL does not represent silence but rather the measurement of a wave with a sound pressure equal to the reference sound pressure [2].
Sound pressure is measured in decibels SPL when the reference above the sound pressure level is applied. There are alternative benchmarks. As a function of fre­quency, the human ear is most acutely attuned to audible sounds between 1 and 5 KHz. One uses the average hearing thresholds for all frequencies to nd a human’s auditory threshold. Hearing levels are expressed in decibels (dB) when these refer­ence values are utilized; a value of 0 dB HL indicates that the measured auditory threshold is equivalent to the average human hearing level at the tested frequency [2].
6 Sound andAcoustics: AnOverview
109

6.4 Psychoacoustics

Hearing and sound are the subjects of psychoacoustics. Investigations into the func­tions of the auditory system, how different parts of sounds inuence perception, and the processes by which sounds are detected and identied are all part of this eld. Understanding the signal is fundamental to the area of psychoacoustics. As part of this process, the spectral and temporal characteristics of the auditory stimuli and their amplitude and point of origin must be described. To address inquiries about hearing, one must know the sound signal. To illustrate this, a psychoacoustician could inquire about the minimum audible volume by asking, “How loud is a tone before it is heard?” A straightforward signal detection test with multiple trials can answer this question. Problems can be signal-plus-noise, in which a tone is pre­sented alongside background noise, or noise-only, in which background noise is the sole element. The listener is then asked to determine if each trial was just noise or if there was both signal and noise. One of the most basic psychoacoustic tests is the tone-detection-in-noise task. Using the listener’s sensitivity (the d’ score or discrim­inability as determined by signal detection theory methods) or percentage of correct responses (PC or percent correct), the psychoacoustician can estimate the signal-to­noise ratio needed for a listener to detect the tone consistently. This unit’s discussion on loudness perception shows that even a seemingly fundamental issue like this can have a complicated response that depends on factors like the signal’s frequency and location [11].
6.4.1 Signal Detection Theory
The application of signal detection theory to derive a trustworthy measure of signal detectability has superseded threshold-nding approaches that attempted to tackle this issue. A bias-free way to quantify sensitivity to any stimulus is provided by signal detection theory [11].
Signal and noise trials are assumed to follow normal distributions in simple sig­nal detection theory. The observer is tasked with determining the likelihood that the data points to a signal or noise trial, given a certain level of signal evidence dis­played on the x-axis (or “internal response” on the graph). The “criterion response” thick line represents the observer’s adoption of a criterion. “Signal” trials are those in which the internal reaction is higher than the criterion, while “noise” trials are those in which it is lower [11].
6.4.2 Level ofDistress fromVarious Pitches
We will go into the critical band in the following unit, but, as a general rule of thumb, it is about one-third of an octave. If we hear two tones simultaneously, which are more than a critical band apart in frequency, the resultant loudness will be approximately equal to the sum of the loudness of the two components. Applying
110
N. Sarı et al.
Stephens’ power law to the intensity of the sum of the loudnesses can approximate the loudness if the two tones are within a critical region. Because the power in Stephens’ power law is <1, the volume of two techniques that are very close together will be quieter than two tones far apart in frequency, presuming that the amplitudes of the two sets of styles are equal [11].
6.4.3 Spectra andVolume
We have shown that the auditory system may affect how loud something is rather than that loudness itself being an absolute entity. Spectral content is another compo­nent that affects loudness alongside frequency. Two tones, one simple (sine tone) and the other more complicated (harmonic), are audible in the following example. Although their waveforms demonstrate equal amplitude, which produces a more substantial audible output? [11]
6.4.4 Time andVolume
The ear does a type of temporal integration in addition to the spectral integration that we just covered. The difference in perceived volume between a short (50ms) and extended (200ms) version of the same sound—with identical amplitude—is because our auditory brains process sounds differently. This effect is practical for noises <250ms but ineffective in sounds more than 250 ms [11].
6.4.5 Determinants ofAmbient Noise Level
Most people will perceive a distant scream as loud, even though the actual ampli­tude of the sound is relatively low because of the distance. We could tell the artist was playing forte rather than piano, even from a great distance, since the tuba’s brightness increased with its volume. A scream has different spectral content and is louder than a speaking voice; the same holds for the human voice. This allows us to deduce the source of a sound (whether it was someone screaming or speaking or the volume of a tubist) and its approximate distance from our ears [11].

References

1. Kurokawa H, Goode RL.Sound pressure gain produced by the human middle ear. Otolaryngol Head Neck Surg. 1995;113(4):349–55.
2. Bruns AD.Middle ear function. In: Meyers AD, editor. Medscape; 2021. Updated: Nov 16, 2021 https://emedicine.medscape.com/article/874456- overview#a1 (Accessed online at July 23, 2023).
3. Schuknecht HF.Pathology of the ear. 2nd ed. Philadelphia: Lea and Febiger; 1993.
6 Sound andAcoustics: AnOverview
4. McJury MJ.Acoustic noise and magnetic resonance imaging: a narrative/descriptive review. J Magn Resonance Imaging. 2022;55(2):337–46.
5. Lin TR, O’Shea P, Mechefske CK.Reducing MRI gradient coil vibration with rib stiffeners. Concepts Magn Reson Part B. 2009;35B:198–209.
6. Brummett RE, Talbot JM, Charuhas P.Potential hearing loss resulting from MR imaging. Radiology. 1988;169:539–40.
7. Liberman MC.Hidden hearing loss: primary neural degeneration in the noise-damaged and aging cochlea. Acoust Sci Tech. 2020;41:59–62.
8. Kohrman DC, Wan G, Cassinotti L, Corfas G.Hidden hearing loss: a disorder with multiple etiologies and mechanisms. Cold Spring Harb Perspect Med. 2020;10:a035493.
9. Hickox AE, Larsen E, Heinz MG, Shinobu L, Whitton JP.Translational issues in cochlear synaptopathy. Hear Res. 2017;349:164–71.
10. The physiology of hearing. Britannica. https://www.britannica.com/science/ear/The-
physiology- of- hearing (Accessed online at July 23, 2023).
11. No authors listed. Unit 3: Fundamentals of Psychoacoustics. https://mutor- 2.github.io/
MUTOR/units/03.html (Accessed online at July 23, 2023).
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Acoustics, Psychoacoustics, andProperties ofSound
MustafaYüksel, OnursalÖnen, andBernhardU.Seeber

7.1 Introduction

Acoustics is the science that investigates the generation, transmission, reception, control, and effects of sound in uids, such as air, and as mechanical waves in elas­tic media. Often, the term “sound” is associated with vibrations that can be per­ceived through our human hearing system—audible sound or “audio” [1]. “Psychoacoustics” derives its essence from the fusion of two disciplines: “psych” referring to psychology, the science of understanding human behavior and percep­tion, and “acoustics,” the study of sound and its transmission. This multidisciplinary eld sits at the intersection of these two realms, focusing on the complex relation­ship between auditory stimuli and their perception. Psychoacoustics is a branch of psychophysics, which investigates the complex perceptual aspects of sound, exam­ining the ways in which individuals perceive auditory stimuli.
In this chapter, we will discuss the fundamental aspects of sound, acoustics, and psychoacoustics from the perspective of otology and audiology. Our emphasis will be on explaining crucial concepts, establishing frequent connections between the­ory and practice, and providing readers with a robust understanding of the key principles.
7
M. Yüksel (*) Department of Audiology, Ankara Medipol University, School of Health Sciences, Ankara, Turkey e-mail: mustafa.yuksel@ankaramedipol.edu.tr
O. Önen Metapax Acoustic, Ankara, Turkey e-mail: oonen@metapax.com.tr
B. U. Seeber Technical University of Munich, School of Computation, Information and Technology, Audio Information Processing, Munich, Germany e-mail: seeber@tum.de
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. T. Kalcioglu et al. (eds.), Otology Updates, Comprehensive ENT,
https://doi.org/10.1007/978-3-031-76173-7_7
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M. Yüksel et al.
7.1.1 What Is Sound?
The denition of sound is conventionally approached from two perspectives: physi­cal and perceptual. Physically, sound is a wave—a mechanical wave that traverses elastic media and, from a vibrating surface, continues as a pressure wave in air before reaching our ears. Elastic media transfer motional energy through their inter­nal structure and return to their original state afterward [2]. From a perceptual angle, sound is what we hear. Anatomically, electric pulses generated in the cochlea, the inner ear, are transmitted via the auditory nerve to brain structures and are subse­quently perceived as sound.
7.1.2 What Is aWave?
According to Webster’s dictionary, a “wave” is dened as “a disturbance or varia­tion that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature.” One famous and easily visu­alized example of a wave is the Mexican wave, commonly observed in stadiums worldwide. In a Mexican wave, a group of people on a hypothetical vertical line stand up and sit back down harmoniously within a few seconds, creating a continu­ous, wavelike motion that travels around the stadium seats.
The term “elastic medium” refers to the people attending the game and sitting in the stadium. This audience is considered “elastic” because, after standing up to cre­ate or transfer the disturbance, they return to their original positions, resembling an elastic material. The people in the stadium do not move with the wave as it travels— they remain at their “equilibrium” positions. The wave, illustrated by a Mexican wave in this example, has distinct characteristics such as speed, representing its travel around the audience; period, indicating the time for it to reach the same line or people; and amplitude, determining how high the audience stands up. In the upcoming sections, we will delve into a detailed exploration of these terms.
7.1.3 What Is theSound Wave WeHear?
The sound wave reaching our ears is a pressure wave that propagates through air. A pressure wave can be described as a change in pressure within the medium it travels through, causing pressure uctuations. Pressure is dened as force per unit area, measured in pascals (Pa), equivalent to newtons (N) divided by area (square meters, m2). However, how does the pressure uctuation in a sound wave take shape?
Air, like any other continuous matter, consists of basic building blocks—mole­cules formed by atoms. While air comprises various molecules such as nitrogen, oxygen, hydrogen, etc., for simplicity and in terms of the size of the molecules and composition of air, we can consider air as a homogeneous mixture of these mole­cules. Visualizing an air column, we can picture randomly dispersed molecules.
7 Acoustics, Psychoacoustics, andProperties ofSound
115
Assume that the air column is excited by the continuous sinusoidal movement induced on the column by the red line back and forth, which creates regions of com­pression and rarefaction of molecules in the medium. In this case, the regions of compression and rarefaction are moving to the right as wavefronts. The depicted motion of the molecules is sinusoidal, which means that the particles and the wave motion follow the pattern of a sine function [2]. Unlike the motion in a Mexican wave, as described in the previous section, the air particles move back and forth in the direction of the wave propagation.

7.2 Fundamental Acoustic Concepts

7.2.1 Speed ofSound
Sound is readily conducted in elastic media such as gases, liquids, and solids. The speed of sound in air at 20°C, and, at sea level, it is 343m/s. Each material, depend­ing on its internal structure, the type of propagating wave, and the environmental or external conditions, has a unique speed of sound. The speed of sound is affected by mechanical properties (such as modulus, density, compressibility), temperature, and humidity. In air, the speed of sound depends strongly on the temperature, increasing
0.6m/s per kelvin temperature increase, and thus on altitude; hence, the temperature should be recorded in acoustic measurements [1, 2]. The speed of sound does not change with frequency, given a specic state and condition.
Solids usually have the highest speed of sound values, followed by liquids. For example, the speed of sound in pure water at sea level is 1481m/s, whereas in steel it is around 6000m/s and in air only 343m/s.
7.2.2 Amplitude ofSound Waves
Acoustic pressure is the deviation from the atmospheric pressure p at sea level). The pressure amplitude of the acoustic wave is pac (Pa), and it corre­sponds to the maximum pressure of the wave that varies between +pac and pac, as seen in Fig.7.1. The actual pressure changes between p
Fig. 7.1 A sinusoidal wave illustrating period. The Y-axis represents pressure, and the X-axis represents time. Period is the time it takes for one complete cycle of the wave
+pac and p
atm
(101.325kPa
atm
pac, but
atm
116
S
cf
()
=
()
×
()
λ
we are only interested in and only hear the variations around the atmospheric equi­librium pressure. Since the average sound pressure is zero and peak amplitudes are hard to dene, sound amplitude is usually measured by rst squaring the instanta­neous amplitude, then averaging it over time, followed by applying the root, thus yielding the root mean square (r.m.s.) amplitude. For sinusoids, it is a factor 0.707 of the peak amplitude. The human ear can sense an acoustic pressure below 20 μPa (20×10−6Pa), i.e., 0 decibel sound pressure level (dB SPL).
M. Yüksel et al.
7.2.3 Period
Period, denoted as T, of any wave is the time it takes for the wave to complete one full cycle or pass through to the same state. The period of a simple sine wave is illustrated in Fig.7.1. Its unit is time, usually expressed in seconds (s).
7.2.4 Frequency
Frequency represents the rate of repetition of a phenomenon or any action within a unit time sequence. In acoustics and many physical sciences, frequency is denoted as the number of repetitions in 1s and can be calculated using the reciprocal of the period T (f= 1/T). Its unit is 1/s, and this unit is referred to as hertz or Hz. The human auditory system is capable of sensing sound in the frequency range of 20–20,000Hz. These values are used for ease of communication, and it is essential to note that this range may vary based on factors such as individual differences, age, and hearing loss. Frequencies below 20 Hz are designated as infrasonic, those between 20 and 20,000Hz are sonic, and those above 20,000Hz are classied as ultrasonic frequencies.
7.2.5 Wavelength
The sine wave depicted in Fig.7.1 represents the time domain. The graph shows pressure variations over time at one specic point in space. However, the wave is also propagating: the pressure change travels. The wavelength (λ) is the distance a wave travels during the time it takes to complete one cycle. In the position domain, it corresponds to the distance between two peaks, as shown in Fig.7.2.
The wavelength of a 100-Hz wave is 3.43m at sea level.
peed of Sound Frequency Wavelength
In
()
=
()
()
/.
ref
Pa
7 Acoustics, Psychoacoustics, andProperties ofSound
Fig. 7.2 A sinusoidal wave illustrating the wavelength. The Y-axis represents pressure, and the X-axis represents distance. The wavelength is the spatial length of one complete cycle of the wave
117
7.2.6 Power andIntensity
Loudspeakers and ampliers are typically rated with a power value: in loudspeak­ers, it reects the input electrical power the loudspeaker can handle without being damaged, and, in ampliers, it is the electrical output power it can maximally deliver. Power reects the amount of energy transferred per second, measured in watts (W).
Power signies the total energy, while intensity, a directional function of power, represents the amount of power passing through a unit area, measured in watts per meter squared (W/m2). Intensity is directional and often relies heavily on the char­acteristics of the sound source. For instance, loudspeakers are designed to project acoustic energy toward the front, resulting in higher acoustic intensity in the frontal direction and less toward the back of the loudspeaker.
tensity IPower WAream
2
7.2.7 Levels andDecibels
In audio, the pressure amplitudes of interest range between 20 μPa and 200Pa, covering the regular hearing range of humans. This presents an eight- order- of­magnitude (108) difference between the largest and smallest amplitudes. Therefore, in acoustics, levels are commonly employed. The decibel is the unit of the decadic logarithmic representation of a quantity relative to a reference value. In acoustics, frequently used levels include sound pressure level (SPL or Lp), sound power level (SWL or LW), and sound intensity level (SIL LI). Reference values for calculations are p
=20×10−6Pa, W
ref
=1×10
ref
level calculations, the root mean square (r.m.s.) values of these quantities are used, and the calculation formulas are provided below:
L
=
10 20 10
p
12
W, and I
2
p
log,
rms
10
p
ref
p
ref
=1×10
12
W/m2, respectively. In
6