Characteristics of sound — pitch loudness and quality

When we hear two different sounds — say, a high whistle and a low drum beat — we can distinguish them even if both are equally loud. We can also tell the difference between the same note played on a violin versus a piano. These differences arise from three fundamental characteristics:

1. Pitch — how high or low the sound seems
2. Loudness — how loud or soft the sound seems
3. Quality (Timbre) — what the sound “sounds like” even at the same pitch and loudness

Each characteristic is linked to a measurable physical property of the sound wave.

Pitch is the characteristic that allows us to distinguish a high-pitched sound from a low-pitched sound.

Pitch depends on the frequency of vibration. Higher frequency → higher pitch. Lower frequency → lower pitch.

• A whistle: high frequency (thousands of Hz) → high pitch
• A bass guitar: low frequency (40–80 Hz) → low pitch
• The human voice: 85–255 Hz for males, 165–255 Hz for females (females have a higher pitch because their vocal cords vibrate at higher frequency)

Range of human hearing: 20 Hz to 20,000 Hz (20 kHz). Sounds below 20 Hz = infrasound (elephants use this). Sounds above 20 kHz = ultrasound (bats, dogs detect this).

Musical scale: The note A4 (concert pitch) = 440 Hz. The octave above (A5) = 880 Hz — exactly double the frequency.

Loudness is how strongly our ears perceive a sound. It depends on the amplitude of the sound wave and on the intensity at our ears.

Intensity is defined as power per unit area: $I = P/A$ (in W/m²).

Decibel scale: Since the range of intensities humans can hear spans a factor of $10^{12}$ (from the threshold of hearing at $10^{-12}$ W/m² to the pain threshold at $10^0 = 1$ W/m²), we use a logarithmic scale:

where $I_0 = 10^{-12}$ W/m² is the threshold of hearing.

Typical values:

• Rustling leaves: ~20 dB
• Normal conversation: ~60 dB
• Busy traffic: ~80 dB
• Rock concert: ~110 dB (near threshold of pain)
• Jet engine at 30m: ~140 dB

Important: Loudness is a subjective perception; intensity is the objective physical quantity. Our ears are not equally sensitive to all frequencies — we hear sounds around 1–4 kHz most easily.

Quality (also called timbre) is the characteristic that lets us distinguish between sounds of the same pitch and loudness produced by different sources.

A note of 440 Hz played on a violin sounds different from the same 440 Hz on a piano, even at the same loudness. Why?

Both produce the same fundamental frequency, but each instrument also produces overtones (harmonics) — multiples of the fundamental — at different relative intensities. The combination of the fundamental plus its overtones creates a unique waveform shape for each instrument.

• Pure tone: Only one frequency (like a tuning fork) — sinusoidal wave
• Musical instrument: Fundamental + multiple harmonics → complex periodic wave

The unique blend of harmonics is the “fingerprint” of each instrument’s sound.

Human speech works the same way: different vowels like “aa,” “ee,” “oo” have the same pitch but different harmonic patterns (the phonation produces different shaped waveforms), which is why we can distinguish them.