1.1 The Discipline of NVH Engineering
1.1.1 Historical Development of Industrial Noise Control
The historical evolution of engineering has been marked by a transition from basic structural survival to dynamic refinement. During the first Industrial Revolution, the primary objective of mechanical design was simply to withstand steady-state and dynamic loads. Steam engines, early textile machinery, and steel structures were heavy, stiff, and massive. Sound and vibration were viewed as unavoidable symptoms of power and industrial progress. The louder the factory, the more productive it was assumed to be.
However, as the speed of machinery increased and the materials became lighter, the dynamic responses of structures began to dominate. High-amplitude vibrations led to fatigue failures, and high noise levels caused hearing loss among workers. By the mid-20th century, the expansion of the automotive and aerospace industries made noise and vibration performance a primary design factor. It was no longer enough for a vehicle or structure to remain intact; it had to operate quietly and smoothly.
In the late 20th century, Noise, Vibration, and Harshness (NVH) emerged as a distinct discipline. This field combined structural dynamics, acoustics, and cognitive psychology to study how mechanical systems generate and transmit energy, and how humans perceive and react to that energy. Today, NVH is critical for product differentiation. A quiet cabin in an automobile or a silent home appliance is associated with high build quality, luxury, and reliable engineering.
1.1.2 Vehicle NVH Categories and Classification
In automotive engineering, NVH is divided into several categories based on the source, path, and receiver:
• Powertrain NVH: Focuses on the noise and vibration generated by the engine, transmission, driveshaft, and differentials. It includes low-frequency engine orders (firing frequencies), combustion noise, gear whine, and transient noises like clutch engagement squeal.
• Road and Tire NVH: Focuses on the interaction between the tire tread and the road surface. This includes structure-borne road noise (low-frequency cabin boom, typically 20 Hz to 200 Hz) and airborne road noise (high-frequency tread hiss, above 500 Hz).
• Aerodynamic (Wind) NVH: Focuses on the noise generated by turbulent airflow over the vehicle's body. It is dominated by high frequencies (above 500 Hz) and becomes the primary source of interior cabin noise at highway speeds (above 100 km/h).
• Brake NVH: Focuses on friction-induced vibrations in the brake system, such as high-frequency brake squeal (typically 1 kHz to 16 kHz) and low-frequency brake groan or shudder.
• Component and Auxiliary NVH: Focuses on noise from subsystem components like the heating, ventilation, and air conditioning (HVAC) fan, radiator cooling fans, wiper motors, window regulators, and electric seat adjusters.
1.1.3 Source-Path-Receiver Architecture
Every NVH problem is analyzed using the Source-Path-Receiver framework:
1.Source: The origin of the dynamic energy. Examples include reciprocating pistons, rotating unbalanced shafts, combustion pressure spikes, tire-road impacts, and turbulent boundary layers.
2.Path: The transmission medium through which the dynamic energy travels from the source to the receiver. Paths are classified into:
• Airborne Path: Sound energy propagates as acoustic waves through the air (e.g., engine radiated noise passing through the engine bay and firewall into the cabin).
• Structure-borne Path: Vibrational energy propagates through solid components (e.g., engine forces passing through engine mounts, subframes, suspension links, and body panels, which then vibrate and radiate sound into the cabin).
3.Receiver: The human observer (e.g., driver, passenger, or bystander) or a sensitive structural component. The receiver's reaction is evaluated using physiological measurements (e.g., hearing thresholds) and psychoacoustic metrics (e.g., loudness, annoyance).
$$\text{Source (Force/Pressure)} \xrightarrow{\text{Path (Structural/Acoustic Transfer)}} \text{Receiver (Human Perception)}$$
1.1.4 NVH Challenges in Electric Vehicles (EVs)
The shift from Internal Combustion Engines (ICEs) to Electric Vehicles (EVs) has introduced new challenges for NVH engineers:
• The Unmasking Effect: The absence of a combustion engine lowers the background noise floor by 10 to 15 dB in the low-to-mid frequency range. However, this unmasks high-frequency noises that were previously hidden, such as wind noise, tire hiss, road hum, and auxiliary component operations (e.g., coolant pumps, battery cooling fans, and HVAC compressors).
• High-Frequency Electromagnetic Noise: Electric motors generate high-frequency tonal noises, commonly referred to as electromagnetic gear whine. This is caused by radial magnetic forces acting across the air gap between the rotor and stator, which excite the motor housing at tooth-passing frequencies (typically in the 1 kHz to 5 kHz range).
• Inverter Switching Noise: The power electronics (inverters) use Pulse Width Modulation (PWM) to control the electric motor. The high-speed switching of transistors (typically at carrier frequencies of 8 kHz, 10 kHz, or 16 kHz) generates high-frequency acoustic tones that can be heard as a sharp hiss.
• Tire Cavity Resonance: The air column inside a tire behaves as a toroidal resonator. Road impacts excite the acoustic cavity of the tire, creating a standing wave (typically around 220 Hz to 250 Hz). In traditional vehicles, this is masked by engine noise, but in EVs, it can cause an annoying cabin boom. This has led to the development of tires with internal acoustic polyurethane foam linings to absorb this cavity resonance.
1.2 Anatomy and Physiology of the Human Auditory System
1.2.1 The Outer Ear
The outer ear is the first stage of the human auditory system. It collects, filters, and directs acoustic waves:
1.Pinna (Auricle): The visible external structure, made of cartilage and skin. The pinna is a directional acoustic filter. Its complex shape introduces spectral notches and peaks in the high-frequency range (above 5 kHz) depending on the direction of the sound source. These spectral modifications are represented mathematically by Head-Related Transfer Functions (HRTFs), which the brain uses to determine the location of a sound source in three-dimensional space.
2.External Auditory Canal: A tube approximately 25 mm to 30 mm long with an average diameter of 7 mm. Closed at the internal end by the eardrum, it acts as a quarter-wave acoustic resonator ($L = \lambda/4$). To calculate its resonant frequency, we apply an end correction for an open cylinder:
$$L_{\text{eff}} = L + 0.6 \cdot r$$
where $r$ is the radius of the canal ($3.5 \text{ mm}$).
$$L_{\text{eff}} = 0.027 \text{ m} + 0.6 \cdot (0.0035 \text{ m}) = 0.0291 \text{ m}$$
The fundamental resonant frequency $f_0$ is:
$$f_0 = \frac{c}{4 L_{\text{eff}}} = \frac{343.2}{4 \times 0.0291} \approx 2948 \text{ Hz}$$
This resonance provides a passive amplification of 10 to 15 dB in the 2 kHz to 4 kHz range, which corresponds to the frequency band containing critical speech information (particularly consonants).
1.2.2 The Middle Ear and Impedance Matching
The middle ear is an air-filled cavity containing the tympanic membrane (eardrum) and three ossicles: the malleus, incus, and stapes. The primary role of the middle ear is to solve the impedance mismatch between the air in the ear canal and the fluid in the inner ear.
Derivation of the Impedance Mismatch Reflection Coefficient
Acoustic impedance ($Z$) is defined as the ratio of acoustic pressure ($p$) to particle velocity ($u$):
$$Z = \rho \cdot c$$
where $\rho$ is the density of the medium and $c$ is the speed of sound.
• For air: $Z_1 = \rho_1 c_1 \approx 413.5 \text{ Pa}\cdot\text{s/m (Rayls)}$
• For the fluid in the cochlea (perilymph, similar to water): $Z_2 = \rho_2 c_2 \approx 1.5 \times 10^6 \text{ Rayls}$
When an acoustic wave traveling in medium 1 strikes the boundary of medium 2, the reflection coefficient for sound intensity ($R_I$) is:
$$R_I = \left( \frac{Z_2 - Z_1}{Z_2 + Z_1} \right)^2$$
Substituting the impedance values:
$$R_I = \left( \frac{1.5 \times 10^6 - 413.5}{1.5 \times 10^6 + 413.5} \right)^2 \approx 0.9989$$
The intensity transmission coefficient ($T_I$) is:
$$T_I = 1 - R_I = 1 - 0.9989 = 0.0011$$
This means only 0.11% of the acoustic energy is transmitted into the fluid, while 99.89% is reflected. This represents an energy loss of:
$$\text{Loss (dB)} = 10 \log_{10}(0.0011) \approx -29.6 \text{ dB}$$
The middle ear acts as a mechanical transformer to overcome this 30 dB loss through two primary mechanisms:
1.The Area Ratio: The effective area of the tympanic membrane ($S_d \approx 55 \text{ mm}^2$) is much larger than the area of the stapes footplate ($S_p \approx 3.2 \text{ mm}^2$). This concentrates the force collected over the eardrum onto a smaller surface:
$$\text{Pressure Ratio} = \frac{S_d}{S_p} \approx \frac{55}{3.2} \approx 17.2$$
2.The Lever Ratio: The malleus and incus rotate about a common axis, forming a lever system. The long process of the malleus is longer than the long process of the incus, providing a mechanical advantage:
$$\text{Lever Ratio} = \frac{L_{\text{malleus}}}{L_{\text{incus}}} \approx 1.3$$
The total mechanical pressure amplification ($G_p$) is:
$$G_p = \frac{S_d}{S_p} \cdot \frac{L_{\text{malleus}}}{L_{\text{incus}}} \approx 17.2 \times 1.3 \approx 22.4$$
Expressing this pressure magnification in decibels:
$$\text{Gain (dB)} = 20 \log_{10}(22.4) \approx 27 \text{ dB}$$
This mechanical gain almost completely offsets the 30 dB impedance mismatch.
*Acoustic Reflex*: The stapedius and tensor tympani muscles contract in response to high-level sounds (above 80 dB SPL). This increases the stiffness of the ossicular chain, reducing the transmission of low-frequency sound energy into the cochlea to protect it from damage.
1.2.3 The Inner Ear and Fluid Dynamics
The inner ear contains the cochlea, a coiled, fluid-filled structure divided into three parallel ducts: the scala vestibuli, the scala tympani, and the scala media. The basilar membrane separates the scala media (which contains endolymph, rich in potassium) from the scala tympani (which contains perilymph, rich in sodium).
When the stapes footplate vibrates against the oval window, it creates pressure waves in the perilymph of the scala vestibuli. Because fluid is incompressible, these waves travel along the scala vestibuli, pass around the apex (helicotrema), and travel back through the scala tympani to bulge the round window membrane. This fluid movement generates a transverse traveling wave along the basilar membrane.
1.2.4 Basilar Membrane Properties and Tonotopic Organization
The basilar membrane acts as a mechanical frequency analyzer. Its physical properties vary along its length:
• At the Base (near the oval window): The membrane is narrow (width $\approx 0.1 \text{ mm}$) and stiff. This makes it resonant to high frequencies.
• At the Apex (near the helicotrema): The membrane is wide (width $\approx 0.5 \text{ mm}$) and compliant. This makes it resonant to low frequencies.
This variation in stiffness ($k$) and mass ($m$) creates a spatial mapping of frequencies along the membrane, known as tonotopic organization. A pure tone generates a traveling wave that increases in amplitude as it propagates along the membrane until it reaches a peak at its resonant location, where it is rapidly attenuated.
Greenwood's Mapping Function
The resonant frequency $f$ (in Hz) can be mapped to the normalized distance $x$ from the apex ($x = 0$ at the apex, $x = 1$ at the base) using Greenwood's function:
$$f(x) = A \left( 10^{a x} - k \right)$$
For humans:
$$f(x) = 165.4 \left( 10^{2.1 x} - 0.85 \right)$$
This relationship shows that the frequency mapping is logarithmic over most of the audible range.
1.2.5 The Organ of Corti and Cochlear Amplifier
The Organ of Corti sits on the basilar membrane and contains two types of receptor cells:
1.Inner Hair Cells (IHCs): Roughly 3,500 cells arranged in a single row. The stereocilia (hairs) on top of the IHCs bend in response to fluid movement, opening potassium channels. This depolarizes the cell, releasing neurotransmitters that trigger action potentials in the auditory nerve fibers.
2.Outer Hair Cells (OHCs): Roughly 12,000 cells arranged in three to four rows. OHCs act as active mechanical amplifiers. They contain the motor protein prestin, which causes the cells to change length in response to electrical potential variations. This electromotility injects mechanical energy back into the basilar membrane vibration, amplifying low-level sounds and sharpening frequency resolution. This active feedback loop is known as the cochlear amplifier.
1.3 Human Hearing Limits
1.3.1 Frequency Limits
The normal frequency range of human hearing is 20 Hz to 20,000 Hz (20 kHz).
• Infrasound (< 20 Hz): These frequencies cannot be heard as sound but can be felt as physical vibrations or pressure variations in the chest cavity and middle ear.
• Ultrasound (> 20 kHz): These frequencies are inaudible to humans but can be detected by other species (e.g., bats, dogs).
• Presbycusis: The progressive loss of high-frequency hearing sensitivity with age. This is caused by the degeneration of hair cells at the base of the cochlea due to cumulative noise exposure and aging. By age 50, the upper hearing limit often drops to 12 kHz - 14 kHz.
1.3.2 Amplitude Limits and Dynamic Range
The human ear can detect a wide range of sound pressures:
• Threshold of Hearing at 1 kHz: The quietest sound a healthy young ear can detect corresponds to an RMS pressure of:
$$p_{\text{ref}} = 20 \ \mu\text{Pa} = 2 \times 10^{-5} \text{ Pa}$$
• Threshold of Pain: The upper limit of hearing, where sound pressure levels cause physical discomfort or pain, corresponds to an RMS pressure of:
$$p_{\text{pain}} = 20 \text{ Pa to } 100 \text{ Pa}$$
• This represents a dynamic range pressure ratio of $10^6$ (one million). Since acoustic power is proportional to the square of pressure ($W \propto p^2$), the ratio of acoustic power between the threshold of pain and the threshold of hearing is:
$$\text{Power Ratio} = \left( 10^6 \right)^2 = 10^{12} \text{ (one trillion)}$$
Logarithmic scales are used in acoustics to simplify calculations across this vast dynamic range.
1.3.3 Just Noticeable Difference (JND)
The Just Noticeable Difference is the smallest change in a sound stimulus that can be detected by a human observer:
• Frequency JND: At mid-frequencies (500 Hz to 2 kHz) and moderate levels (above 40 dB SPL), the frequency JND is approximately 0.3% of the carrier frequency. For example, a listener can easily distinguish between 1,000 Hz and 1,003 Hz.
• Level JND: For pure tones, the JND in sound pressure level is approximately 1 dB at low-to-moderate levels, and can drop to 0.5 dB at high levels. In NVH engineering, a 3 dB change is generally considered the minimum change required to be clearly noticeable to an average listener in an automotive or industrial environment.
1.4 Equal-Loudness Contours & Phon/Sone Scales
1.4.1 Fletcher-Munson, Robinson-Dadson, and ISO 226
The human ear's sensitivity varies with frequency. To map this relationship, researchers have conducted subjective listening tests to define equal-loudness contours:
• Fletcher and Munson (1933): Conducted the first major study using headphones to present pure tones and reference tones at 1 kHz to a pool of test subjects.
• Robinson and Dadson (1956): Refined the curves using speakers in an anechoic chamber (free-field listening) rather than headphones. This work was adopted as the first international standard, ISO 226.
• ISO 226:2003: The current international standard, which updated the curves based on newer, multi-national research that corrected discrepancies in the Robinson-Dadson data (particularly at low frequencies).
1.4.2 The Phon Scale
The Phon is the unit of subjective loudness level. By definition: > The loudness level of any sound in Phons is equal to the Sound Pressure Level (SPL) in dB of an equally loud 1,000 Hz pure tone.
For example, a 100 Hz pure tone that is subjectively matched in loudness to a 1,000 Hz tone at 40 dB SPL has a loudness level of 40 Phons, even though its physical sound pressure level must be approximately 60 dB SPL.
1.4.3 The Sone Scale (Linear Loudness)
The Phon scale is logarithmic, meaning it does not scale linearly with human perception. A sound of 80 Phons does not sound twice as loud as a sound of 40 Phons. The Sone scale was developed to create a linear scale for perceived loudness:
• 1 Sone is defined as the loudness of a 1,000 Hz pure tone at a level of 40 dB SPL (40 Phons).
• For loudness levels above 40 Phons, a 10 Phon increase corresponds to a doubling of perceived loudness:
$$S = 2^{\frac{L_N - 40}{10}}$$
where $S$ is the loudness in Sones, and $L_N$ is the loudness level in Phons.
1.5 Acoustic Metrics and Scales (SPL, SWL, SIL)
1.5.1 Sound Pressure and SPL ($L_p$)
Sound pressure is the dynamic local deviation from ambient atmospheric pressure caused by an acoustic wave. We use the Root-Mean-Square (RMS) pressure ($p_{\text{rms}}$) to calculate the sound level, as the time-average of a sinusoidal pressure wave is zero.
$$L_p = 10 \log_{10}\left(\frac{p_{\text{rms}}^2}{p_{\text{ref}}^2}\right) = 20 \log_{10}\left(\frac{p_{\text{rms}}}{p_{\text{ref}}}\right) \text{ dB SPL}$$
where $p_{\text{ref}} = 20 \ \mu\text{Pa} = 2 \times 10^{-5}$ Pa (in air).
2. Sound Power Level (SWL, $L_w$)
Sound power ($W$) is the total acoustic energy radiated by a source per unit time.
$$L_w = 10 \log_{10}\left(\frac{W}{W_{\text{ref}}}\right) \text{ dB}$$
where $W_{\text{ref}} = 10^{-12} \text{ W} = 1 \text{ pW}$ (one picowatt). *Note on notation*: To avoid confusion with Sound Pressure Level ($L_p$), Sound Power Level is often written as $L_w$ or $L_W$.
3. Sound Intensity Level (SIL, $L_I$)
Sound intensity ($I$) is a vector quantity defined as the rate of sound energy transmission per unit area in a specified direction.
$$L_I = 10 \log_{10}\left(\frac{I}{I_{\text{ref}}}\right) \text{ dB}$$
where $I_{\text{ref}} = 10^{-12} \text{ W/m}^2$ (in air).
The Relationship in a Free Field
In a free field (an environment with no reflections, such as an anechoic chamber or open air), the sound intensity $I$ in the direction of wave propagation is directly related to the square of the RMS sound pressure:
$$I = \frac{p_{\text{rms}}^2}{\rho_0 c}$$
where $\rho_0$ is the density of the fluid and $c$ is the speed of sound. The product $\rho_0 c$ is the characteristic acoustic impedance of the medium.
• For air at $20^\circ\text{C}$ and standard atmospheric pressure ($101.325$ kPa):
$$\rho_0 \approx 1.204 \text{ kg/m}^3, \quad c \approx 343.2 \text{ m/s}$$
$$\rho_0 c \approx 1.204 \times 343.2 \approx 413.2 \text{ Pa}\cdot\text{s/m (Rayls)}$$
• Let us calculate the sound pressure level ($L_p$) when the intensity is exactly at the reference level ($I = I_{\text{ref}} = 10^{-12} \text{ W/m}^2$):
$$p_{\text{rms}}^2 = I \cdot \rho_0 c = 10^{-12} \times 413.2 = 4.132 \times 10^{-10} \text{ Pa}^2$$
$$p_{\text{rms}} = \sqrt{4.132 \times 10^{-10}} \approx 2.033 \times 10^{-5} \text{ Pa} \approx 20.3 \ \mu\text{Pa}$$
• This shows that the reference pressure $p_{\text{ref}} = 20 \ \mu\text{Pa}$ and the reference intensity $I_{\text{ref}} = 10^{-12} \text{ W/m}^2$ are aligned. Under standard atmospheric conditions, the sound pressure level and sound intensity level are practically equal:
$$L_p \approx L_I$$
1.6 Frequency Weighting Filters
Because human hearing sensitivity varies with frequency, raw physical sound pressure level measurements (expressed in linear dB) do not correlate well with perceived loudness. To address this, international standards (IEC 61672-1) define frequency-weighting filters that shape the measured spectrum to match the human ear's response at different levels.
The Standard Weighting Curves
• A-Weighting ($dB(A)$): Based on the inverse of the 40-Phon equal-loudness curve. It attenuates low frequencies significantly (-39.4 dB at 31.5 Hz) and introduces a slight boost around 2.5 kHz (+1.2 dB). Although originally designed for low-level sounds, A-weighting is now widely used for all sound levels in occupational noise regulations (OSHA, NIOSH) and environmental noise standards.
• B-Weighting ($dB(B)$): Based on the inverse of the 70-Phon curve, representing medium-level sounds. It has a flatter low-frequency response than A-weighting but is rarely used in modern standards.
• C-Weighting ($dB(C)$): Based on the inverse of the 100-Phon curve, representing high-level sounds. It has a very flat response across the audible range, rolling off only at the frequency extremes (below 31.5 Hz and above 8 kHz). It is typically used to assess low-frequency rumble, peak impact noise (e.g., explosions), and machinery noise where low-frequency vibration is high.
• D-Weighting ($dB(D)$): Specifically designed to measure aircraft noise, with a boost between 2 kHz and 8 kHz to account for the high-frequency whine of turbojet engines. It has largely been replaced by perceived noise level (PNL) metrics.
• Z-Weighting ($dB(Z)$): "Zero" or flat weighting. It represents the unweighted, linear physical sound pressure level over a defined frequency band (typically 10 Hz to 20 kHz).
| Frequency (Hz) | A-Weighting (dB) | B-Weighting (dB) | C-Weighting (dB) |
|---|
| ---------------- | ------------------ | ------------------ | ------------------ |
| 10 | -70.4 | -38.2 | -14.3 |
| 20 | -50.5 | -24.2 | -6.2 |
| 31.5 | -39.4 | -17.1 | -3.0 |
| 63 | -26.2 | -9.3 | -0.8 |
| 125 | -16.1 | -4.2 | -0.2 |
| 250 | -8.6 | -1.3 | 0.0 |
| 500 | -3.2 | -0.3 | 0.0 |
| 1000 | 0.0 | 0.0 | 0.0 |
| 2000 | +1.2 | -0.1 | -0.2 |
| 4000 | +1.0 | -0.7 | -0.8 |
| 8000 | -1.1 | -2.9 | -3.0 |
| 16000 | -6.6 | -8.4 | -8.5 |
1.7 Psychoacoustic Metrics Overview
While frequency-weighting filters provide a basic approximation of human hearing, they are limited by their static, linear design. They do not account for temporal variations, spectral masking, or the complex processing of the human brain. To capture these effects, the field of psychoacoustics uses more advanced metrics:
1. Loudness (Sone and Phon)
Loudness calculations (standardized in ISO 532) model the non-linear processing of the cochlea.
• Zwicker's Method (ISO 532-1): Designed for steady-state or time-varying sounds. It filters the signal into 1/3 octave bands, maps these bands to the Bark scale (which represents the critical bands of the cochlea), models spectral masking (how a loud tone masks adjacent quiet tones), and integrates the specific loudness ($N'$) across the critical bands to compute the overall loudness in Sones.
• Critical Bands: The cochlea can be modeled as a series of band-pass filters called critical bands. If two sounds fall within the same critical band, they mask each other, and their perceived loudness is less than the sum of their individual loudnesses. If they are in different critical bands, their loudnesses sum directly.
2. Sharpness (Acum)
Sharpness measures the relative high-frequency content of a sound. A sound with dominant energy at high frequencies (above 3 kHz) is perceived as sharp, metallic, or piercing.
• The unit of sharpness is the Acum.
• 1 Acum is defined as the sharpness of a narrow-band noise centered at 1 kHz with a bandwidth of one critical band, presented at a level of 60 dB.
• Sharpness ($S$) is calculated using a weighted integration of specific loudness:
$$S = c \cdot \frac{\int_{0}^{24 \text{ Bark}} N'(z) \cdot g(z) \cdot dz}{\int_{0}^{24 \text{ Bark}} N'(z) \cdot dz}$$
where $g(z)$ is a weighting function that increases at higher Bark values ($z > 16$ Bark, or frequencies above 3 kHz). Sharpness is an important metric for evaluating the quality of sounds like electric motor whine, vacuum cleaners, and wind noise.
3. Roughness (Asper)
Roughness is a subjective sensation caused by rapid amplitude or frequency modulation in a sound.
• It occurs when the modulation frequency is between 20 Hz and 300 Hz, peaking around 70 Hz.
• A classic example of roughness is a helicopter rotor or a lawnmower engine.
• The unit of roughness is the Asper.
• 1 Asper is defined as the roughness of a 1,000 Hz pure tone that is 100% amplitude-modulated at a frequency of 70 Hz, presented at a level of 60 dB.
• At these high modulation frequencies, the ear cannot follow the individual temporal envelopes, resulting in a rough, harsh sensation rather than distinct fluctuations.
4. Fluctuation Strength (Vacil)
Fluctuation strength is similar to roughness but occurs at lower modulation frequencies, below 20 Hz (peaking around 4 Hz).
• At these slow speeds, the ear can track the individual variations in the sound level (e.g., a slow siren, or an engine idling at 240 RPM).
• 1 Vacil is defined as the fluctuation strength of a 1,000 Hz pure tone that is 100% amplitude-modulated at a frequency of 4 Hz, presented at a level of 60 dB.
5. Prominence Ratio (PR) and Tone-to-Noise Ratio (TNR)
These metrics (standardized in ECMA-74) quantify the audibility of discrete tones in a background of broadband noise.
• A common example is the high-frequency whine of a computer cooling fan or a vehicle alternator.
• If a tone is prominent, it is highly audible and annoying, even if its sound pressure level is far below the overall broadband level.
• Tone-to-Noise Ratio (TNR) compares the power of the tone to the total power of the noise within a critical band centered on the tone.
• Prominence Ratio (PR) compares the total power in the critical band containing the tone to the average power of the two adjacent critical bands. A tone is generally considered prominent if the ratio exceeds 9 dB at high frequencies.
1.8 Interactive Visualizations
The following interactive vector diagrams illustrate these concepts:
Figure 1: Fletcher-Munson and ISO 226 Equal-Loudness Curves
This diagram shows the relationship between physical sound pressure level (dB SPL) and subjective loudness level (Phons) across the audible frequency spectrum.