S2 · Supportive Knowledge (HVAC and Refrigeration)

Foundation lesson · 18 minute study session

Add sound energy, then choose the control path.

Keep logarithmic levels, transmission paths and vibration frequency separate.

By the end of this lesson

Combine independent sound levels logarithmically.
Distinguish sound power from sound pressure at a stated receiver.
Recognize resonance and the need for an appropriate isolation model.

Decibels are logarithmic.

Adding independent source contributions requires adding the underlying energy measures, not their decibel numbers. Use levels of the same kind with the same reference and measurement conditions. Two equal uncorrelated contributions increase the combined level by about 3 dB.

Source strength is not receiver level.

Sound power describes a source; sound pressure depends on distance, room absorption, directivity and other propagation conditions. A manufacturer sound-power rating cannot be used as receiver sound pressure without a stated acoustic model. Duct paths, casing radiation and structure-borne transmission can need different controls.

Vibration control depends on frequency.

A rotating speed in rpm becomes a forcing frequency in hertz by dividing by 60 for a once-per-revolution disturbance. Compare that frequency with the system natural frequency. Near resonance, motion can be amplified. An isolator selection requires its load, stiffness, damping and stated transmissibility model; reducing sound at the source does not automatically remove a structural vibration path.

A decision map for this lesson

Match the source, path and receiver

Sound levels and vibration ratios require different models and compatible reference quantities.

Choose the governing relationship and catch the wrong route
Condition or question	Governing decision	Error to avoid
Independent sound contributions at one receiver	Add energies: $L_{sum}=10\log_{10}\sum 10^{L_i/10}$ .	Adding the decibel values arithmetically.
Source sound power is compared with receiver sound pressure	Use the applicable propagation/room model and matching receiver conditions.	Subtracting them directly because both are stated in dB.
Forcing frequency and mount frequency are supplied	Use $r=f/f_n$ in the stated isolation model, including damping when required.	Assuming isolation improves monotonically through resonance.
Rigid connections bypass resilient mounts	Check the complete structure-borne transmission path.	Treating the mount rating as proof that every pipe and duct connection is isolated.

On a narrow screen, scroll across the table to compare the decision and the error.

Relationships and their limits

Independent equal-reference sound levels

L_{total}=10\log_{10}\left(\sum_i10^{L_i/10}\right)

Independent or uncorrelated sources; matching level definitions and receiver conditions. Not a coherent-phase sum.

Once-per-revolution forcing

f=N/60;\qquad r=f/f_n

N in rpm, f and natural frequency $f_{n}$ in Hz. Other disturbance orders have different forcing frequencies.

Symbols and unit basis
Symbol	Meaning	Units or basis
$L$	Sound level on stated common basis	dB
$N$	Rotational speed	rpm
$f$	Forcing frequency	Hz
$f_n$	Natural frequency	Hz
$r$	Frequency ratio	dimensionless

One decision, fully worked

Apply the method.

At the same receiver, two independent machines produce sound-pressure levels of 64 dB and 60 dB on the same measurement basis. Background is negligible. Separately, a once-per-revolution disturbance comes from a 900 rpm machine mounted on a system with natural frequency 5 Hz.

Add sound contributions in the energy domain.
Factor out the larger level for an easily checked calculation.
Convert rpm to Hz before comparing with the natural frequency.

L_{total}=64+10\log_{10}(1+10^{(60-64)/10})=65.46\ \mathrm{dB}

f=900/60=15\ \mathrm{Hz};\qquad r=15/5=3

Decision

Combined sound-pressure level is about 65.46 dB. The separate vibration frequency ratio is 3; a transmissibility or isolation percentage still requires an appropriate model.

Independent check

The total is higher than 64 dB but below 67.01 dB, the result for two equally loud 64 dB independent sources. Frequency ratio is dimensionless.

Specialist extension

Treat sound levels and vibration ratios as physical models

For independent sound sources on the same acoustic basis, add energies before converting back to decibels. Sound power and sound pressure describe different quantities and cannot be interchanged without the relevant propagation model. For ideal undamped force isolation, transmissibility depends on frequency ratio; real damping and support flexibility change the response, especially near resonance. Use any supplied isolation model with its assumptions.

A new applied case

Two independent sources each produce 60 dB at the same receiver under the same conditions. Separately, an ideal undamped isolator has natural frequency 5 Hz and forcing frequency 20 Hz.

L_{total}=10\log_{10}(10^{60/10}+10^{60/10})=63.010\ \mathrm{dB}

r=20/5=4;\quad T=\left|1/(1-r^2)\right|=1/15=0.06667

Decision. The summed level is about 63.01 dB. Under the separate ideal isolator model, force transmissibility is 0.06667.

Cross-check. Adding decibel numbers gives a false 120 dB. Near r = 1, the undamped model becomes singular and cannot represent a finite damped response.

Unit basis. L is dB on one acoustic basis; frequency is Hz; r and force transmissibility T are dimensionless.

ASHRAE Pocket Guide for Air Conditioning, Heating, Ventilation, Refrigeration, SI, 9th ed. (2017), printed pp. 276 and 284, supporting acoustics and vibration fundamentals. Original cases use an explicitly qualified ideal model; the guide is not an examination reference.

Open targeted practice in the study studio →

Transfer the method

Supportive Knowledge (HVAC and Refrigeration) · HV-LC-S2

Try a new decision.

Select one

An enclosure has independent equal machines, each producing 60 dB at the same receiver. The combined level is 66.02 dB on a common reference basis. Background is negligible. How many operating machines does this measurement indicate?

A6 machinesB4 machinesC10 machinesD2 machines

A lesson check supports practice, not a readiness score. Your response stays in this page session and clears on reload.

Catch the common errors

Adding 64 and 60 arithmetically to report 124 dB.
Combining a sound-power rating directly with a receiver sound-pressure level.
Comparing rpm with a natural frequency in Hz without converting.

Handbook navigation drill

Find it, then explain it.

Search: Sound Levels; Vibration Isolation

Locate the decibel combination relationship and the vibration-isolation guidance. Identify what receiver and frequency data the problem must supply.

Check your navigation

Section 9.7 covers sound; section 9.8 provides vibration guidance. Neither an rpm value nor a sound level alone establishes isolator performance.

Reference path: §9.7–9.8, pp. 536–545. These are printed handbook page numbers; section names and search terms remain the primary navigation method. See technical review status.

Theory sources

NCEES PE Mechanical Reference Handbook v2.1: §9.7–9.8, pp. 536–545
Mechanical and Electrical Equipment for Buildings, 12th ed.: mechanical systems and energy principles. Supporting theory; not an examination reference.

Worked examples and lesson prose are original ReasonSpan^™ material. Obtain authorized publications separately; this preview does not reproduce the supplied books or handbook.