A sound-level meter passes its reference check. Later, turning its microphone changes the high-frequency reading. Those observations can both be correct: the reference check and the field measurement test different conditions.
This guide explains how microphone orientation enters a measurement, why a single calibration tone cannot establish the whole frequency response, and how an angle mismatch can distort a reported total. All numerical responses below are invented teaching data, not correction values for a commercial microphone.
eduKateSG · The Gold Standard of Acoustics
Choose your reading route
Understand the calibration condition · Chapters 1–2. Build the quantities before using a formula.
Correct a spectrum and test the limits · Chapters 3–5. Follow original examples, assumptions and changed conditions.
Audit the setup and transfer · Chapters 6–8. Test transfer, answer common questions and follow connected reading.
Full chapter index · Practice and evidence checks · Return to Acoustics
Chapter index
Understand the calibration condition · Chapters 1–2
Correct a spectrum and test the limits · Chapters 3–5
Audit the setup and transfer · Chapters 6–8
CHAPTER 1 OF 8 · Understand the calibration condition
1. Start with the pressure you want to measure
A microphone converts a pressure disturbance into an electrical signal. To turn that signal into a physical quantity, we need a relationship between input and output. Sensitivity, commonly expressed in volts per pascal, supplies part of that relationship.
But “the pressure” needs a location and a condition. We might want the pressure that would exist at a point in a sound field before the microphone was placed there. Alternatively, a pressure calibration may refer to the pressure acting at its diaphragm in a coupler. These definitions cannot be exchanged without considering the microphone’s response.
The microphone is a physical object. At sufficiently high frequencies, its size is no longer negligible compared with the wavelength. Its body and diaphragm can alter the local field through scattering. The voltage then depends on how the sound approaches it as well as on the incident pressure.
The GRAS guide to free-field, pressure and random-incidence microphones explains the different response designs. A free-field microphone is intended to compensate for its disturbance of an approaching field under specified conditions. Random-incidence response addresses sound arriving from many directions.
Before calculating, finish this sentence: “I want to estimate the sound pressure at this position, over these frequencies, under this field condition.” That statement determines which response information is relevant.
CHAPTER 2 OF 8 · Understand the calibration condition
2. Read the angle on the calibration information
Angle of incidence describes the direction from which the wave arrives relative to a defined microphone axis. Do not assume the angle printed on one diagram uses the same convention as another. Locate the diaphragm, reference axis and direction of travel on the manufacturer’s drawing.
For the teaching model here, 0° means a wave approaching directly toward the diaphragm along its normal axis. An angle of 90° means side incidence. These are definitions for this article, not instructions to point every microphone in the same direction.
The Brüel & Kjær measurement-microphone primer explains why changing orientation can invalidate the corrections associated with a specified incidence angle. Its older product and standards listings should not be treated as current purchasing or compliance guidance; the physical distinction remains useful.
What a passing reference check establishes
A compatible acoustic calibrator supplies a defined signal under defined coupling conditions. A successful check can reveal whether the measurement chain’s sensitivity at that check condition is consistent with expectations.
It does not independently test every frequency, every angle, the room’s reflections, or all accessories used later. A 1 kHz check cannot by itself demonstrate that an 8 kHz side-incidence response is correct. This is an inference about the scope of the test, not a criticism of calibration.
Record the check frequency, equipment, gain settings and applicable procedure. Then separately record the field orientation. Both records matter because they answer different questions.
CHAPTER 3 OF 8 · Correct a spectrum and test the limits
3. Correct two bands before combining them
Define response error R as displayed level minus the desired incident level. A negative R means the system reads low. Under this definition, corrected level = displayed level − R.
Imagine a steady field measured with an instrument whose selected compensation assumes 0° incidence. The actual incidence is 90°. A suitable calibration model gives the following residual errors after that selected compensation.
| Frequency band | Displayed level | Assumed residual error R | Corrected level |
|---|---|---|---|
| Band near 1 kHz | 70.0 dB | 0.0 dB | 70.0 dB |
| Band near 8 kHz | 66.0 dB | −4.0 dB | 70.0 dB |
The sign check is valuable. A system reading 4 dB low needs 4 dB added to the displayed level. Subtracting another 4 dB would move farther from the desired value.
For non-overlapping bands expressed with the same pressure reference and compatible averaging, combine their mean-square contributions:
L_total = 10 log₁₀(10^(L₁/10) + 10^(L₂/10)).
The displayed total is 10 log₁₀(10⁷ + 10^6.6), approximately 71.46 dB. After correcting each band, the total becomes 10 log₁₀(10⁷ + 10⁷), approximately 73.01 dB.
The broadband error is therefore about −1.55 dB. It is neither the 8 kHz error of −4 dB nor the arithmetic average of the two band errors, −2 dB. Each band contributes a different amount of measured energy to the sum.
This example assumes that the response error is effectively constant within each band. A wide band containing a sharp response feature needs finer spectral treatment. Also retain any intended frequency weighting consistently; an unweighted total and an A-weighted total answer different questions.
CHAPTER 4 OF 8 · Correct a spectrum and test the limits
4. Change the spectrum and the total error changes
Now keep the same microphone, orientation and response errors, but change the source. Its true low-frequency band is 80 dB and its true high-frequency band is 60 dB. The displayed bands become 80 dB and 56 dB.
The true total is about 80.043 dB; the displayed total is about 80.017 dB. The difference is only about −0.026 dB within this idealised calculation. The high-frequency band still has the same −4 dB error, but it contributes little to the overall energy.
Reverse the spectrum: true bands of 60 dB and 80 dB display as 60 dB and 76 dB. The true total remains about 80.043 dB, while the displayed total is about 76.108 dB. The total error is now nearly −3.94 dB.
These three cases explain why an apparently satisfactory broadband comparison can hide a serious spectral mismatch. Agreement for one source does not prove agreement for another source with a different frequency distribution.
Keep the correction identifiable
Retain the uncorrected band data, the response convention, the selected compensation and the corrected result. If software has already applied a correction, applying it again is another error.
A useful report names the measurand and the correction source. “Corrected level” alone is incomplete: another analyst needs to know which physical mismatch was corrected and which uncertainties remain.
CHAPTER 5 OF 8 · Correct a spectrum and test the limits
5. Recognise when one angle is insufficient
A reflected field may contain arrivals from several directions. One source location does not imply one arrival direction at the microphone. A strong wall reflection can reach the diaphragm from an angle very different from the direct path.
Consider a deliberately simplified band containing mutually uncorrelated contributions: 60% of the true mean-square pressure arrives from a direction with 0 dB response error, and 40% from a direction with −4 dB error. The measured-to-true energy ratio is:
0.60 × 1 + 0.40 × 10^(−4/10) ≈ 0.759.
Its level error is 10 log₁₀(0.759), about −1.20 dB. Using the correction for either direction alone would misrepresent this mixture.
The 60/40 split is an assumption, not something recoverable from one broadband level. If coherent reflections interfere, phase relationships and the microphone’s complex response matter; this simple energy-weighted model is no longer enough.
Other limits include an unknown windscreen response, a changed protective grid, obstruction by the operator, movement of the diaphragm, overload and background contamination. An angle correction cannot repair all of these at once.
The PTB free-field microphone calibration description illustrates how a controlled comparison transfers a reference sensitivity. The lesson for a field survey is to document the conditions under which its calibration relationship is being used.
CHAPTER 6 OF 8 · Audit the setup and transfer
6. Test the setup with a controlled comparison
A meaningful orientation check changes direction while holding the diaphragm’s measurement position, source output and analysis settings as stable as possible. Rotating around the end of a long handle can move the diaphragm through a spatial interference pattern. That would combine a position effect with an angle effect.
| Evidence to retain | What it helps distinguish |
|---|---|
| Photograph or drawing of diaphragm position and axis | Rotation from unintended translation |
| Before-and-after reference checks | Sensitivity drift from field-response differences |
| Frequency-resolved readings and source stability record | Spectral mismatch from source changes |
| Microphone, accessories and selected correction mode | Physical configuration from software compensation |
Use suitable established procedures for real measurements. A student can practise the reasoning with the invented table without generating high sound levels or claiming a phone recording is a calibrated noise survey.
Changed-context check
A third band displays 65 dB and has R = +2 dB. What is its corrected value? It is 63 dB: this time the system reads high. Explain the sign before using a calculator.
Next, suppose a microphone is rotated but both low- and high-frequency readings change equally by 6 dB. Does this prove an angle mismatch? No. Source output, position, gain and other causes remain possible. The observed pattern should be compared with a documented response model and an independently controlled setup.
Finally, a report contains only the total level from the first example. Can you reconstruct its corrected total? Not uniquely. You need the spectral contributions and relevant response information. Several different spectra can produce the same displayed total.
CHAPTER 7 OF 8 · Audit the setup and transfer
7. Questions that prevent common mistakes
Is an omnidirectional microphone equally sensitive at every frequency and angle?
An ideal omnidirectional model is useful, but a real microphone has finite dimensions and a specified response. Read its frequency-dependent data and tolerances.
Should every free-field microphone point straight at the source?
Use the orientation and correction specified for the instrument and measurement method. The source may also contribute through multiple paths. A universal pointing rule would ignore those conditions.
Does calibration remove uncertainty?
No. Calibration characterises a relationship with stated conditions and uncertainty. Using it outside those conditions introduces another question that a certificate alone cannot resolve.
Can I average the correction values in decibels?
That does not generally produce the correct total-level correction. Correct compatible spectral components, combine their mean-square contributions, and preserve the measurement’s intended weighting and bandwidth.
Is the largest angle correction always the most cautious answer?
It may produce a bound only if a justified model supports that use. Applying an arbitrary worst value to every band can be misleading. State the available evidence and uncertainty instead of manufacturing precision.
CHAPTER 8 OF 8 · Audit the setup and transfer
8. Continue from sound physics to defensible measurements
Build the physical model
- The Gold Standard of Acoustics connects waves, pressure, interference, spectra and measurement.
- Microphones, polar patterns, decibels and distance develops directionality and the wider recording chain.
- Sound, decibels and hearing exposure distinguishes level arithmetic from time and exposure measures.
Follow another measurement limitation
- Background subtraction and unstable source estimates explains why a small residual can be highly uncertain.
- T20, T30 and decay-time estimates examines what a fitted decay segment can establish.
Carry the checking habit into another subject
The Gold Standard of Education connects this worked reasoning to learning that transfers. How X Works provides the wider explanatory routes.
The manufacturer primer, GRAS guide and PTB calibration description linked above were checked on 22 October 2026. They support the physical and calibration distinctions. Every response value, band level and directional energy split in the examples is an original teaching assumption. Use actual equipment documentation for a real correction.