Human hearing spans a limited frequency window — roughly 20 Hz to 20,000 Hz. Below that window lies infrasound (felt as a rumble more than heard). Above it lies ultrasound (inaudible to us, but used by bats for echolocation and by doctors for imaging).
Beyond the limits of normal wave behavior lies a different phenomenon entirely: shock waves, which form when an object outruns the sound it’s producing. The sonic boom of a fighter jet is the everyday example.
This section gives you the relevant numbers and the basic physics of each regime.
The Frequency Spectrum of Sound
Category
Frequency range
Examples
Infrasound
< 20 Hz
Earthquakes, elephant communication, large explosions
Audible sound
20 Hz – 20,000 Hz
Speech, music, environmental noise
Ultrasound
> 20,000 Hz (20 kHz)
Medical imaging, bat echolocation, sonar
Human hearing sensitivity declines with age — especially at the high-frequency end. Most adults can’t hear above about 15,000–17,000 Hz, while a teenager with healthy ears can hear close to 20,000 Hz.
Ultrasound in Medicine
Key medical applications of ultrasound:
Prenatal imaging — visualizing a developing fetus without using ionizing radiation (a huge advantage over X-ray for soft tissues).
Echocardiography — imaging heart chambers and valves in real time.
Doppler ultrasound — measuring blood flow velocity using the Doppler shift of reflected waves (covered in §7.8).
Lithotripsy — using focused ultrasound shock waves to break up kidney stones non-invasively.
Shock Waves and the Mach Number
When a sound source moves faster than the speed of sound in the medium, it outruns its own waves. The wave fronts pile up into a cone-shaped pressure front called a shock wave. You hear this as a sonic boom when the cone passes over your ears.
A common misconception: a sonic boom isn’t a one-time event when the plane “breaks the sound barrier.” The shock cone trails behind the plane continuously whenever it’s supersonic, and anyone who hears the cone passing over them hears a boom — even though the plane has been supersonic for hours. That’s why the FAA banned supersonic flight over land for civilian aircraft like the Concorde — every flight would have boomed every house along the path.
A jet travels at 680 m/s through air where the speed of sound is 340 m/s. What is its Mach number? Does a shock wave form?
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Mach 2; yes, a shock wave forms.M=680/340=2. Since $M > 1$, the jet is supersonic — it outruns its own sound waves, creating a cone-shaped pressure front (sonic boom).
Why does medical ultrasound use high frequencies (1–20 MHz) rather than audible frequencies?
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Higher frequencies → shorter wavelengths → better spatial resolution. You can resolve smaller structures than with longer wavelengths. Audible-frequency wavelengths would be tens of centimeters long — too large to image any anatomical detail. The trade-off: higher frequencies are absorbed faster by tissue, so they don't penetrate as deeply. Choose frequency based on what you're trying to image.
A bat emits ultrasound at 50 kHz with λ=? in air (v=340 m/s)? Why is shorter wavelength helpful for echolocation?
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λ=6.8 mm.λ=v/f=340/50,000=0.0068 m = 6.8 mm. The short wavelength lets the bat resolve insect-sized prey — wavelengths shorter than the target give clear echoes. A wavelength much larger than the target would diffract around it and produce no useful echo.
