Sound Fundamentals

Sound Pressure and Sound Pressure Level

Sound pressure represents the instantaneous deviation from atmospheric pressure caused by acoustic waves. This parameter forms the basis of all acoustic measurements in HVAC systems.

Sound Pressure

Sound pressure (p) is measured in Pascals (Pa) and represents the root-mean-square (RMS) pressure fluctuation:

• Range: 20 μPa (threshold of hearing) to 200 Pa (threshold of pain)
• Typical HVAC equipment: 0.02 to 2 Pa
• Measured with microphones calibrated to standard reference conditions

Sound Pressure Level (SPL)

Due to the wide range of audible pressures, a logarithmic scale is used:

SPL = 20 log₁₀(p/p₀) dB

Where:

• p = measured sound pressure (Pa)
• p₀ = reference pressure = 20 μPa (2 × 10⁻⁵ Pa)
• dB = decibels

The reference pressure of 20 μPa corresponds to the threshold of human hearing at 1000 Hz. This logarithmic scale compresses the million-to-one pressure ratio into a manageable 0 to 120 dB range.

Key SPL Values

Sound Power and Sound Power Level

Sound power represents the total acoustic energy radiated by a source per unit time, independent of distance or room characteristics.

Sound Power

Sound power (W) is measured in watts and represents the fundamental output of a noise source:

• Independent of measurement distance
• Independent of room acoustics
• Intrinsic property of the source
• Cannot be measured directly; calculated from pressure measurements

Sound Power Level (PWL)

PWL = 10 log₁₀(W/W₀) dB

Where:

• W = sound power (watts)
• W₀ = reference power = 10⁻¹² watts (1 picowatt)

Sound power level provides a standardized method for comparing equipment noise emissions. Manufacturers typically specify equipment PWL in octave bands.

Relationship Between Power and Pressure

For a point source in free field:

SPL = PWL - 20 log₁₀(r) - 11 dB

Where r = distance in meters. This relationship shows SPL decreases 6 dB per doubling of distance from the source.

Decibel Mathematics

The decibel scale follows logarithmic addition rules that differ from linear arithmetic.

Adding Sound Levels

When combining multiple uncorrelated noise sources:

L_total = 10 log₁₀(10^(L₁/10) + 10^(L₂/10) + … + 10^(Lₙ/10)) dB

Quick reference:

• Equal levels: Add 3 dB (two 80 dB sources = 83 dB)
• 10 dB difference: Add 0.4 dB (80 dB + 70 dB = 80.4 dB)

• 15 dB difference: Add 0 dB (dominant source controls)

Subtracting Sound Levels

To determine equipment contribution in ambient noise:

L_equipment = 10 log₁₀(10^(L_total/10) - 10^(L_background/10)) dB

This calculation is valid only when total level exceeds background by at least 3 dB. Below 3 dB, measurements lack sufficient accuracy.

Frequency Analysis

Sound frequency determines pitch and significantly affects human perception and material transmission characteristics.

Frequency Ranges

HVAC systems typically generate noise across the 63 Hz to 8000 Hz range, with dominant energy often in the 125 Hz to 2000 Hz bands.

Octave Band Analysis

Octave bands divide the audible spectrum into standardized frequency ranges for analysis and specification.

Octave Band Centers

The standard octave band center frequencies:

Each octave band has an upper frequency limit twice the lower limit (f₂ = 2f₁). The center frequency equals the geometric mean: f_c = √(f₁ × f₂).

One-Third Octave Bands

For detailed analysis, each octave band subdivides into three bands with center frequencies related by the cube root of 2 (1.26):

• 100 Hz, 125 Hz, 160 Hz (within 125 Hz octave band)
• Provides finer resolution for identifying specific noise sources
• Used for detailed troubleshooting and equipment diagnostics

Frequency Spectrum Characteristics

Broadband Noise: Energy distributed across multiple frequency bands

• Generated by turbulent airflow, fans, diffusers
• Relatively smooth spectrum without distinct peaks
• Perceived as “whoosh” or “rush”

Tonal Noise: Energy concentrated at discrete frequencies

• Generated by fan blade pass, motor speed, resonances
• Distinct peaks in spectrum
• Perceived as hum, whine, or whistle
• More annoying than broadband noise at equal level

Pure Tone Penalty: When tonal components dominate:

• Add 3-5 dB penalty to measured level
• Recognizes increased annoyance of tonal character
• Applied in NC, NCB, and RC rating methods

A-Weighting

A-weighting applies frequency-dependent corrections that approximate human hearing sensitivity.

A-Weighting Curve

The human ear exhibits reduced sensitivity at low and high frequencies. A-weighting compensates:

Application in HVAC

A-weighted sound level (dBA) provides a single-number rating:

• Correlates better with subjective loudness than unweighted levels
• Used for community noise ordinances and building codes
• Tends to de-emphasize low-frequency rumble
• May underestimate annoyance of low-frequency HVAC noise

Limitations

A-weighting has known limitations for HVAC applications:

• Underweights low frequencies (<200 Hz)
• Does not account for tonal character
• NC, RC, and NCB curves provide better assessment for occupied spaces

Sound Transmission

Sound transmission describes how acoustic energy passes through building elements and air paths.

Transmission Loss (TL)

Transmission loss quantifies the sound reduction provided by a barrier:

TL = 10 log₁₀(1/τ) dB

Where τ = transmission coefficient (ratio of transmitted to incident power).

Mass Law Approximation: TL ≈ 20 log₁₀(mf) - 48 dB

Where:

• m = surface mass (kg/m²)
• f = frequency (Hz)

This relationship shows TL increases 6 dB per doubling of mass or frequency.

Sound Transmission Class (STC)

STC provides a single-number rating of transmission loss:

• Based on standardized frequency range (125-4000 Hz)
• Higher numbers indicate better sound isolation
• Typical values: STC 25 (poor) to STC 65 (excellent)

Flanking Paths

Sound bypasses direct transmission through multiple paths:

• Ductwork without adequate attenuation
• Plenum spaces above partitions
• Structural connections between spaces
• Gaps around doors and penetrations

Proper acoustic design addresses all transmission paths, not just primary barriers. A small unsealed gap can reduce partition effectiveness by 5-10 dB.

Duct Breakout and Break-in

Sound transmission through duct walls:

• Breakout: Sound escapes from duct into surrounding space
• Break-in: External noise enters duct system
• Controlled by duct wall mass, stiffness, and damping
• Rectangular ducts transmit more readily than round ducts
• Duct lagging improves transmission loss by 5-15 dB

Measurement Considerations

Accurate acoustic measurements require proper technique:

Microphone Placement

• Minimum 1 meter from reflective surfaces
• Multiple positions to average spatial variation
• Height appropriate to occupant ear level (1.2-1.5 m seated)

Background Noise

• Measured with equipment off
• Must be at least 10 dB below equipment noise for accuracy
• 3-10 dB difference requires correction

Environmental Factors

• Wind speed <5 m/s for outdoor measurements
• Temperature and humidity affect high-frequency propagation
• Barometric pressure affects calibration

Application to HVAC Systems

Understanding sound fundamentals enables effective noise control:

1. Use octave band data for diagnostic accuracy
2. Address low-frequency content with appropriate constructions
3. Recognize that A-weighted levels may not capture full impact
4. Consider all transmission paths in design
5. Apply mass law for quick estimates of required barriers
6. Account for pure tone penalties when present
7. Measure at representative occupant locations