Hertz ↔ dB A-Weighting: Understanding Human Hearing
Discover how our ears perceive different frequencies and why sound measurements need frequency weighting!
What is Frequency? (Hertz – Hz)
Frequency determines the pitch of sound – how high or low it sounds to our ears.
Definition: 1 Hertz (1 Hz) means one complete sound wave cycle occurs every second.
Frequency Units and Their Applications:
- Hz (Hertz): 1 cycle/second – Used for audio frequencies, human hearing (20-20,000 Hz)
- kHz (Kilohertz): 1,000 Hz – Audio equipment specs, radio AM band (540-1600 kHz)
- MHz (Megahertz): 1,000,000 Hz – FM radio (88-108 MHz), TV channels, WiFi
- GHz (Gigahertz): 1,000,000,000 Hz – Microwave ovens (2.4 GHz), cell phones, radar
Sound Frequency Examples:
- Bass Frequencies: 20-250 Hz (bass guitar, kick drum, thunder)
- Mid Frequencies: 250-4000 Hz (human voice, piano, most music)
- High Frequencies: 4000-20,000 Hz (cymbals, bird songs, whistle)
- Concert A: 440 Hz (musical tuning standard)
- Human Voice: 85-255 Hz (male), 165-255 Hz (female)
What are Decibels? (dB)
Decibels (dB) measure the intensity or loudness of sound on a logarithmic scale.
Key Concept: Our ears don’t perceive all frequencies equally! We’re most sensitive around 1000-4000 Hz and less sensitive to very low and very high frequencies.
Understanding A-Weighting:
A-weighting adjusts sound measurements to match human hearing perception
- 0 dB: Maximum sensitivity (around 1000 Hz)
- -10 dB: Good sensitivity (2000-5000 Hz)
- -20 dB: Reduced sensitivity (500 Hz, 8000 Hz)
- -40 dB: Poor sensitivity (100 Hz, 16000 Hz)
- -70 dB: Very poor sensitivity (20 Hz, 20000 Hz)
Real-World Sound Levels:
- Whisper: 30 dB (very quiet)
- Normal Conversation: 60 dB (comfortable)
- Traffic: 80 dB (loud)
- Rock Concert: 110 dB (very loud)
- Jet Engine: 140 dB (painful/damaging)
The Science of A-Weighting
A-weighting was developed to make sound measurements match how loud sounds actually seem to human ears. It’s based on extensive research into human hearing sensitivity.
A-Weighting Mathematical Formula:
A(f) = 20 × log₁₀(Ra(f))
Where Ra(f) is the complex frequency response function
Key Characteristics:
- Peak Response: 0 dB at 1000 Hz (our most sensitive frequency)
- Low Frequency Roll-off: Strong attenuation below 500 Hz
- High Frequency Roll-off: Gradual attenuation above 5000 Hz
- Human-Centered: Matches our hearing sensitivity curve
Why A-Weighting Matters:
- Our ears evolved to be most sensitive to speech frequencies (1-4 kHz)
- We perceive low frequencies (bass) as much quieter than they actually are
- Very high frequencies also seem quieter due to hearing limitations
- Sound level meters use A-weighting to give “human-relevant” measurements
- This helps in noise control, audio engineering, and hearing protection
Applications of Frequency Weighting
Environmental Noise
City planners use A-weighted measurements to assess noise pollution because it reflects how annoying sounds actually are to people.
Audio Engineering
Recording engineers use frequency weighting to make mixes that sound balanced across the frequency spectrum to human ears.
Hearing Protection
Safety engineers use A-weighted levels to determine when hearing protection is needed, as it predicts hearing damage risk.
Speaker Design
Speaker manufacturers optimize frequency response considering A-weighting to create more natural-sounding audio systems.
Practice Problems for Students
Problem 1: Human Voice Frequency
Question: A male voice has a fundamental frequency of 125 Hz. What is the A-weighted response?
Click to see solution
Solution: A-weighted response ≈ -16.2 dB
Explanation: This shows why bass voices can sound quieter than they measure – our ears are less sensitive to low frequencies!
Problem 2: Musical Note A4
Question: Concert A (440 Hz) is used for tuning. What’s its A-weighted response?
Click to see solution
Solution: A-weighted response ≈ -2.5 dB
Explanation: Close to 0 dB because 440 Hz is in our most sensitive hearing range!
Problem 3: High-Frequency Cymbal
Question: A cymbal produces strong energy at 8000 Hz. What’s the A-weighted response?
Click to see solution
Solution: A-weighted response ≈ -1.1 dB
Explanation: Still near our peak sensitivity, which is why cymbals cut through a mix so well!
Frequency Response Reference
Common Frequencies and A-Weighted Response:
| Frequency | A-Weight (dB) | Sensitivity | Common Sources |
|---|---|---|---|
| 20 Hz | -50.5 dB | Very Poor | Earthquake vibrations, organ pedals |
| 31 Hz | -39.4 dB | Very Poor | Deep bass, thunder |
| 125 Hz | -16.2 dB | Poor | Male voice, bass guitar |
| 500 Hz | -3.2 dB | Good | Female voice, piano |
| 1 kHz | 0.0 dB | Best | Reference frequency, speech clarity |
| 4 kHz | +1.0 dB | Best | Speech consonants, presence |
| 8 kHz | -1.1 dB | Very Good | Cymbals, brilliance |
| 16 kHz | -6.6 dB | Fair | Air, ultra-high frequency |
| 20 kHz | -8.5 dB | Poor | Upper limit of human hearing |
| 40 kHz | -22.5 dB | Very Poor | Ultrasonic cleaning, dog whistles |
| 100 kHz | -40.2 dB | Very Poor | Medical ultrasound imaging |
| 1 MHz | -80.0 dB | Extremely Poor | AM radio upper range |
