Human Range of Hearing

When a loudspeaker cone vibrates, it alternately compresses and rarefies the air in front of it, creating a longitudinal pressure wave. The number of compression–rarefaction cycles per second is the frequency f, measured in hertz (Hz). The human brain interprets frequency as pitch: higher frequency → higher pitch. The relationship between frequency f, wave speed v, and wavelength λ is v = fλ. In air at 20 °C, sound travels at approximately 343 m s⁻¹, so a 20 Hz tone has a wavelength of about 17 m, while a 20 kHz tone has a wavelength of only 17 mm.

By convention, the human audible range is taken as 20 Hz ≤ f ≤ 20 000 Hz. Think of it like the visible spectrum in optics: just as the eye cannot detect infrared or ultraviolet light, the ear cannot detect infrasound or ultrasound. The 20 Hz lower limit corresponds to the mechanical resonance properties of the basilar membrane in the cochlea at its widest end; the 20 kHz upper limit corresponds to the narrowest end. In practice, most adults over 25 lose sensitivity above 15–16 kHz, and many elderly people cannot hear above 8–10 kHz — a process called presbycusis.

Infrasound (f < 20 Hz) is produced by earthquakes, volcanic eruptions, ocean waves, large atmospheric storms, and some industrial machinery. Although inaudible as a tone, very intense infrasound can be felt as vibration in the chest. Elephants and whales use infrasound for long-distance communication — low-frequency waves travel farther with less absorption because attenuation in air increases with frequency. Infrasound monitoring networks are used globally to detect nuclear explosions under the Comprehensive Nuclear-Test-Ban Treaty.

Ultrasound (f > 20 kHz) is inaudible to humans but used extensively in medicine (diagnostic imaging at 1–20 MHz), industrial non-destructive testing, and animal communication. Bats echolocate using frequencies of 20–100 kHz; dogs can hear up to about 65 kHz. In medical ultrasound, the short wavelengths at high frequencies allow resolution of fine anatomical detail — a 5 MHz wave in tissue has a wavelength of about 0.3 mm. The piezoelectric effect is used to both generate and detect ultrasonic pulses.

The physics of the cochlea explains both boundaries. The basilar membrane inside the cochlea acts as a mechanical frequency analyser — different positions along its 35 mm length resonate at different frequencies (tonotopy). Hair cells at the apex (wide, floppy end) respond to low frequencies; those at the base (narrow, stiff end) respond to high frequencies. Below 20 Hz, the membrane cannot complete a resonant cycle efficiently; above 20 kHz, the stiffness of the basilar membrane's base and the inertia of the middle-ear ossicles prevent adequate energy transfer.

• v — Wave speed (m s⁻¹): Speed at which the sound wave propagates through the medium; approximately 343 m s⁻¹ in air at 20 °C.
• f — Frequency (Hz (s⁻¹)): Number of complete pressure oscillations per second; determines the pitch perceived by the listener.
• \lambda — Wavelength (m): Distance between successive compressions (or rarefactions) in the wave; inversely proportional to frequency at constant speed.

Problem. A dog whistle produces a sound at 25 000 Hz (25 kHz). (a) Is this audible to humans? (b) Calculate the wavelength of this sound in air, given that the speed of sound in air is 340 m s⁻¹.

Answer. The dog whistle is ultrasonic and inaudible to humans. Its wavelength in air is 13.6 mm.

• Wave Speed, Frequency and Wavelength — The equation v = fλ directly connects frequency to wavelength for any sound wave, making it essential for calculating wavelengths within or outside the audible range.
• Longitudinal and Transverse Waves — Sound is a longitudinal pressure wave; understanding this wave type explains how compressions and rarefactions create the oscillations the ear detects.
• Intensity and the Decibel Scale — Perceived loudness depends not only on frequency (pitch) but also on amplitude (intensity); the decibel scale quantifies how loud a sound is across the audible range.
• Ultrasound Applications — Ultrasound lies immediately above the human audible range; medical and industrial uses of ultrasound rely on understanding why these frequencies exceed the hearing limit.