2.1 Frequency and pitch

Frequency and pitch are key concepts in acoustics. Frequency measures sound wave oscillations, while pitch is how we perceive those frequencies. The relationship between them is logarithmic, with each octave requiring a doubling of frequency.

Our ears are finely tuned to detect a wide range of frequencies. From the low rumble of a bass drum to the high notes of a flute, different instruments and voices produce unique frequency ranges that our auditory system processes into recognizable sounds.

Frequency and Pitch in Acoustics

Frequency and pitch perception

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• Frequency measures number of cycles or oscillations per second in Hertz (Hz)
• Pitch represents subjective perception of frequency by human ear
• Higher frequencies generally perceived as higher pitches creating direct correlation
• Pitch perception follows logarithmic nature requiring doubling of frequency for each octave increase

Frequency calculation from period

• Period represents time for one complete wave cycle measured in seconds
• Frequency and period have inverse relationship expressed by formula $f = \frac{1}{T}$
• Example: 0.005 second period yields $f = \frac{1}{0.005} = 200$ Hz frequency

Human ear and frequency perception

• Outer ear collects sound waves, middle ear transmits vibrations, inner ear contains cochlea
• Cochlea's fluid-filled spiral structure houses basilar membrane for frequency-to-place coding
• High frequencies resonate at cochlea base, low frequencies at apex
• Hair cells convert mechanical vibrations to electrical signals stimulating auditory nerve fibers
• Auditory cortex processes signals integrating information to perceive pitch

Frequency ranges of instruments and voice

• Human hearing spans approximately 20 Hz to 20,000 Hz
• Adult male voice: 85-180 Hz, adult female: 165-255 Hz, child: 250-300 Hz
• Piano covers 27.5 Hz to 4,186 Hz, violin 196 Hz to 3,136 Hz
• Guitar ranges 82 Hz to 1,318 Hz, flute 262 Hz to 2,349 Hz
• Bass drum produces low frequencies 30 Hz to 147 Hz
• Instrument classification based on frequency ranges: bass (low), tenor and alto (mid-range), soprano (high)