3.6.12 · D5Spacecraft Structures & Systems Engineering
Question bank — Acoustic loads — SPL, octave band analysis
This is a rapid-fire concept check for Acoustic Loads — SPL, Octave Band Analysis. Each line is a Question ::: Answer reveal. Cover the card, say your reasoning out loud, then reveal. If your answer is a bare "yes/no" without a because, count it as a miss — the whole point of acoustics is understanding why the logs and squares behave the way they do.
True or false — justify
Every decibel (dB) below refers to Sound Pressure Level relative to .
Two uncorrelated 140 dB sources combine to 280 dB.
False. Decibels are logarithms of intensity, and logs don't add linearly; uncorrelated sources add in intensity, so doubling gives only dB → 143 dB.
A +6 dB change means the sound pressure has doubled.
True. Since and , +6 dB is exactly a factor-2 rise in (but a factor-4 rise in intensity).
A +6 dB change means the acoustic intensity has doubled.
False. Intensity , so +6 dB (pressure ×2) means intensity ×4. It is +3 dB that doubles intensity, because .
The OASPL of a spectrum is just the arithmetic average of its octave-band levels.
False. You must convert each band to intensity, sum them, then convert back: . The sum is dominated by the loudest band, not the mean.
Adding a band that is 20 dB quieter than the peak changes the OASPL by less than 0.1 dB.
True. A 20 dB deficit means the intensity of the peak; adding 1% to the total intensity raises the level by dB — negligible.
Increasing the SPL by 3 dB requires you to double the number of identical uncorrelated engines.
True. Each doubling of independent sources adds intensity, and dB, regardless of the starting level.
The 632 Pa peak pressure at 150 dB would crush the spacecraft like a vice.
False. It is a small oscillating modulation on top of Pa atmosphere (about 0.6%); the danger is fatigue and resonance from the shaking force, not static crushing.
A one-third-octave analysis of the same launch spectrum always reports a lower OASPL than octave analysis.
False. OASPL is the total energy however you slice it; finer bands just redistribute the same intensity, so the summed OASPL is unchanged (up to rounding).
Spot the error
Find the flaw in each statement.
"To combine two 145 dB sources, average their pressures: Pa, so still 145 dB."
The error is averaging pressures. Uncorrelated pressures add in quadrature (), giving Pa → 148 dB, not 145.
"SPL uses because the reference is a pressure."
Backwards. SPL uses because it references pressure; the 20 comes from , so of pulls the exponent 2 out front. Intensity level uses .
"An octave band centered at 500 Hz runs from 250 Hz to 750 Hz."
The limits are wrong. The band spans to , i.e. 354 Hz to 707 Hz, whose ratio is exactly 2:1. 250–750 Hz has a ratio of 3:1.
"The band center is the arithmetic mean of the limits: ."
It is the geometric mean: . That makes the band logarithmically centered, matching how we hear and how frequency ratios (octaves) work.
"Because pressures add, two 632 Pa waves give 1264 Pa, i.e. +6 dB."
Only correlated, in-phase waves add pressures directly. Launch acoustic sources are uncorrelated, so intensities add and the rise is +3 dB, not +6 dB.
"The reference pressure is arbitrary, so SPL numbers have no physical anchor."
It is not arbitrary: it corresponds to W/m² via , the human threshold of hearing at 1 kHz. It fixes 0 dB.
"Acoustic loads and mechanical vibration are the same test, so we only need one."
They excite differently: mechanical vibration enters through mounting points, while acoustic loads press on all exposed surfaces at once — see 3.6.11 Random Vibration — PSD, Miles' Equation for the mounting-point route and 3.6.14 Combined Environmental Testing for why both matter.
Why questions
Why does SPL use a logarithmic scale at all?
Human-relevant pressures span roughly to Pa — a 10-million-fold range. Logarithms compress this into a readable 0–140 dB, and match the roughly multiplicative way we perceive loudness.
Why do intensities (not pressures) add for uncorrelated launch sources?
With random relative phase, the cross-term in time-averages to zero, leaving . Since , the intensities — the energy carriers — simply sum.
Why does the OASPL usually sit only a few dB above the loudest single band?
Because the sum is dominated by the largest term; quieter bands contribute exponentially less intensity, so their combined effect adds at most a few dB.
Why do we care which octave band holds the most energy, rather than just the OASPL?
A structure amplifies violently only near its natural frequency. Energy in a band that lands on that resonance does far more damage than the same energy elsewhere — see 3.6.10 Structural Natural Frequencies and Mode Shapes.
Why is (the characteristic impedance) the quantity linking pressure to intensity?
For a plane wave, pressure and particle velocity obey , so is the "acoustic resistance." It turns the pressure squared into transmitted power: . See 2.5.8 Acoustic Impedance and Transmission.
Why is the band center defined as the geometric mean of the limits?
So the band is symmetric in log-frequency: equal musical/octave distance on each side. Arithmetic centering would bias every band toward its high-frequency edge.
Why can acoustic loads produce amplification factors of 10–50× in a thin panel?
At resonance the panel's response is set by its quality factor ; a lightly damped panel (–) stores energy each cycle, so a modest pressure builds into large displacements before losses catch up.
Edge cases
What is the SPL when exactly?
dB. The reference pressure is defined as the 0 dB point (threshold of hearing), not silence.
What does the SPL formula give for perfect silence, ?
, so SPL dB. Mathematically it never reaches a finite floor; physically, background noise always sets a real, finite minimum.
What is the OASPL if every one of bands has the identical level ?
. All bands add in intensity, so equal bands raise the total by dB.
Combining a 150 dB source with a 100 dB source — what is the result?
Essentially 150 dB. The quieter source is 50 dB down ( of the intensity), so it adds dB — undetectable.
Two perfectly correlated, in-phase identical sources — how much do they add?
+6 dB. Correlated pressures add directly (), and . This is the correlated exception to the usual +3 dB rule.
Two identical sources exactly out of phase (180°) at the same point — what happens?
They cancel: , so SPL there. Real fields are only partially correlated, so full cancellation happens at isolated nodes, not everywhere.
What OASPL do you get from a single band?
Exactly that band's level: . With one term the log and exponent undo each other — a useful sanity check on the summation formula.
If a band's level is reported as " dB" (no energy), how does it affect the OASPL?
Not at all: contributes nothing to the intensity sum, so the OASPL is unchanged. Empty bands are silent partners.
Recall One-line rules to carry away
+3 dB ::: doubles intensity (two uncorrelated equal sources). +6 dB ::: doubles pressure (or two correlated in-phase sources). +10 dB ::: ten times the intensity. +20 dB ::: ten times the pressure. OASPL ::: dominated by the loudest band, always any single band.
Next stops: 3.6.13 Shock Loads and SRS for the transient cousin of these steady-state loads, and 3.6.14 Combined Environmental Testing for how acoustic, random-vibration, and shock environments are qualified together.