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Octave Band A-Weighting Calculator

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About This MicroSim

A fan's sound power is published in eight octave bands, centered at 63, 125, 250, 500, 1,000, 2,000, 4,000 and 8,000 Hz. To compare band data with an A-weighted limit, add the standard A-weighting correction to each band and add the weighted bands logarithmically:

  • Weighted band = band level + A-weighting correction
  • LwA = 10 log10(Σ 10^(weighted/10)), rounded to 0.1 dB
  • Unweighted overall = 10 log10(Σ 10^(L/10))

The corrections are the standard IEC 61672 octave-band values: −26.2, −16.1, −8.6, −3.2, 0, +1.2, +1.0 and −1.1 dB. The bar chart draws each band's unweighted level as an outline; after Check, the A-weighted level fills each bar, the largest contributor is outlined in orange and labeled, and the two totals appear beside a dashed line at the limit. The limit line spans only the totals, because a limit on the overall level says nothing about any single band.

Three challenges, in this fixed order (all spectra illustrative):

# Bands 63 to 8,000 Hz (dB) Limit (dB, A-weighted) Model LwA (dB) Verdict
1 98, 96, 94, 90, 87, 83, 78, 72 95 92.5 Meets
2 90, 92, 95, 97, 96, 93, 88, 82 95 100.2 Exceeds
3 105, 100, 92, 86, 82, 78, 74, 68 95 90.0 Meets

Challenge 1 is the chapter's worked example: 92.5 dB A-weighted against 101.6 dB unweighted, with the 500 and 1,000 Hz bands dominating. A challenge is correct when the level you type is within ±0.5 dB of the model value (rounded to 0.1 dB) and the meets/exceeds choice is right. You get two attempts. If the level you type matches the unweighted total or the arithmetic average of the bands, the feedback says so. After a second wrong attempt the model value and the weighted band table are shown and the challenge counts as missed. Mastery is 3 of 3 on the first attempt.

After challenge 3, free mode unlocks: each band slider runs from 50 to 110 dB in 1 dB steps (starting at challenge 1's spectrum) and the limit from 70 to 110 dB (starting at 95 dB). The weighted values, both totals, the verdict, the largest contributor and the change from the starting spectrum update as you move a slider. Free mode is never scored.

How to Use

  1. Read challenge 1's eight band levels and the limit. Work out the weighted bands and the logarithmic sum with a calculator.
  2. Type the overall A-weighted level in LwA (dB), choose Meets or Exceeds, and press Check.
  3. Read the feedback. A correct answer reads "✓ Correct: LwA = 92.5 dB, which meets the 95 dB limit." in a solid green box; a wrong one starts with "✗ Not quite." in a dashed red box. Use the second attempt if one is left.
  4. Press Next challenge and repeat. "Challenges correct: n of 3" keeps the running score.
  5. After challenge 3, press Start free mode. Raise the 63 Hz band by 10 dB and note the change in LwA; press Reset bands, raise the 1,000 Hz band by 10 dB and compare. Start over clears the score and returns to challenge 1.

Keyboard: Enter checks the answer and then goes to the next challenge. M picks Meets and E picks Exceeds when the cursor is not in the answer box (Tab to the radio buttons and use the arrow keys or Space works too). Tab reaches every slider; the arrow keys move a focused slider.

Data label: "Illustrative spectra · A-weighting: IEC 61672 octave-band values", at the bottom left of the drawing.

Iframe Embed Code

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<iframe src="https://moroshek.github.io/FanTASTIC-textbook/sims/ch27-octave-band-a-weighting/main.html"
        height="797px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

The learner will calculate the overall A-weighted sound power level from eight octave band levels and judge it against a limit, to within ±0.5 dB (Bloom: Apply, verb: calculate).

Audience

Adult professional development: new application engineers, sales staff, representatives and facilities staff.

Duration

10-15 minutes

Prerequisites

  • Octave band and sound power level (Chapter 25 and the Octave Band Sound Data section of Chapter 27)
  • A-weighting and logarithmic addition of decibels
  • Noise limits and their forms (Chapter 27, Noise Limits)

Activities

  1. Challenges (6-8 min): Solve the three spectra with a calculator before pressing Check. Write down the weighted value of each band and which band is largest after weighting.
  2. Review (2 min): Compare the A-weighted and unweighted totals for challenge 3. Explain why the 105 dB band at 63 Hz does not control the A-weighted total.
  3. Free mode (3-5 min): Raise the 63 Hz band by 10 dB, then reset and raise the 1,000 Hz band by 10 dB. Record the change in LwA each time and decide which band a silencer should attack.

Common Misconceptions Addressed

  • The overall level is the arithmetic average or sum of the band levels: the feedback names the average when you type it, and the totals bar shows the logarithmic sum.
  • The loudest unweighted band controls the A-weighted total: challenge 3 and the free-mode 63 Hz test show that a loud low band barely moves LwA.
  • An unweighted overall level can be compared with an A-weighted limit: challenge 1's unweighted 101.6 dB would wrongly fail the 95 dB limit; the feedback names the unweighted total when you type it.

Assessment

  • The running line "Challenges correct: n of 3" counts challenges solved on either attempt. At the end the sim shows "First-attempt score: n of 3" and the mastery line; mastery is 3 of 3 on the first attempt, with the level within ±0.5 dB and the verdict right.
  • Follow-up: a limit of 90 dB applies to challenge 1's fan. Which two bands would you attenuate, and roughly how much?

References

  1. A-weighting - Wikipedia article on the A-weighting curve and its octave-band corrections.
  2. Octave band - Wikipedia article on octave bands and their center frequencies.
  3. Sound power - Wikipedia article on sound power level, the source quantity a fan catalog publishes.
  4. Twin City Fan product specifications - CSI-format guide specifications, including the Model RTF section 23 34 16 that asks for sound power in eight octave bands with an A-weighted overall value.
  5. FanPedia: The Fan & Blower Encyclopedia - Twin City Fan's reference on fan sound and selection.