Examqo › Examqo library › Speech-language pathology and audiology › Hearing science
Acoustics and decibels: calculations, SPL versus HL versus SL, resonance, filters and room acoustics
Most acoustics questions are a short calculation: the decibel is a logarithmic ratio, so you add intensities, not decibels. A handful of rules is enough — 10log for intensity, 20log for pressure, the inverse square law, converting between SPL, HL and SL, tube resonance and the Sabine equation.
Why it matters in the exam
The rules that recur in the bank: doubling pressure adds 6 dB and doubling intensity 3 dB; ten times the intensity is 10 dB and ten times the pressure 20 dB; 1 pascal is 94 dB SPL, and 0.2 pascal is 80 dB SPL (reference 20 micropascals). Two equal incoherent sources add 3 dB; N identical sources add 10log(N); a 6 dB gap between two sources adds about 1 dB to the louder; and to remove background noise you subtract intensities. In a free field each doubling of distance takes off 6 dB, but in a room, beyond the critical distance, the reflected field is nearly uniform and the level stops falling.
The scale questions: the HL scale exists because normal threshold in SPL differs from frequency to frequency, so the audiometer removes a reference value (RETSPL) at each frequency; dB SPL = dB HL + RETSPL. Sensation level (SL) is measured above the person's own threshold — 40 dB SL above an SRT of 35 is 75 dB HL. Wavelength = speed of sound over frequency (500 Hz in air — 0.68 m); the speed of sound rises with elasticity and falls with density; the resonant frequency of a mass-spring system falls as mass rises (4 times the mass — half the frequency). With a high-pass filter of 12 dB per octave, a tone 2 octaves below cut-off is attenuated by 24 dB. Sabine reverberation time: 0.161 times volume over absorption; classrooms should be at most 0.6 seconds with background noise at most 35 dBA, and children with hearing loss need an SNR of at least +15 dB.
Key points
- Pressure 20log, intensity 10log; 1 pascal = 94 dB SPL.
- Sources add by intensity: equal +3, N identical +10log(N).
- Doubling distance in a free field: −6 dB.
- SPL = HL + RETSPL; SL above one's own threshold.
- Sabine RT60; classroom up to 0.6 seconds, SNR of +15 for children with hearing loss.
Summary table
| Rule | Formula or value | Example from the bank |
|---|---|---|
| Pressure and intensity | Pressure: 20log; intensity: 10log | Doubling pressure = +6; doubling intensity = +3 |
| Adding sources | Add intensities; N identical: 10log(N) | 60 plus 60 = 63; four to five machines = about +1 |
| Distance in a free field | −6 dB per doubling of distance | From 0.5 to 4 m: 3 doublings = −18 |
| HL, SPL and SL | SPL = HL + RETSPL; SL above one's own threshold | 30 dB HL + 25.5 = 55.5 dB SPL |
| Wavelength and resonance | λ = c ÷ f; closed tube: c ÷ 4L | 500 Hz = 0.68 m; a 1.6 cm canal — about 5300 Hz |
| Filters | Slope in dB per octave; bandwidth = upper minus lower | 707–1414 Hz: an octave band around 1000 Hz |
| Rooms | RT60 = 0.161 × V ÷ A; standing waves | Classroom: up to 0.6 seconds; in sound field use warble tones |
A free exam question
A point sound source in a free field produces 70 dB SPL at 1 meter. What will the level be at 2 meters?
- A. 67 dB SPL
- B. 64 dB SPL
- C. 35 dB SPL
- D. 70 dB SPL
In the full version for subscribers
- A simple algorithm
- Memory aid
- Exam traps
- 5 review cards
- What matters for the exam
The full version is open to subscribers of: Speech and hearing (communication disorders).
Subscriber? Read the full topic Plans and prices 25 free questions
Sources
- Speaks, Introduction to Sound, 3rd edition (1999) — Decibels, resonance, filters
- ANSI/ASA S12.60, 2010 — Acoustical Performance Criteria, Design Requirements and Guidelines for Schools
- ISO 389-1 and ANSI/ASA S3.6, 2017 / 2018 — Reference equivalent threshold sound pressure levels and audiometer specification
Sources are given for further reading; the text is written afresh and not copied from them.
Reviewed by the Examqo AI Professor · 2026-11-02. The text may contain errors; when in doubt, check the source.