6 Waves and Sound in Biology and Medicine

Oscillations and their measures

An oscillation is repeated motion around an equilibrium position. The time needed for one complete cycle is the period, represented by $T$. The number of cycles per second is the frequency, represented by $f$, and measured in hertz (Hz). These quantities are reciprocals:

The amplitude describes the size of the oscillation. For sound, greater pressure amplitude generally means greater intensity. Period, frequency, and amplitude describe different aspects of a vibration: how long a cycle takes, how often cycles occur, and how large the motion is.

How sound waves travel

A wave carries energy through a medium without transporting the medium as a whole. Sound is a mechanical, longitudinal wave: particles of the medium move back and forth in the direction the wave travels. This motion creates alternating compressions and rarefactions.

Wave speed $v$, frequency $f$, and wavelength $\lambda$ are related by:

Sound speed depends on the medium. When sound enters a different medium, its frequency remains set by the source, while its speed and wavelength may change. Sound requires a medium and cannot travel through a vacuum.

Example: A tuning fork vibrating at $500\ \text{Hz}$ has a period of $\frac{1}{500}\ \text{s}=0.002\ \text{s}$, or $2\ \text{ms}$. If sound travels through air at about $340\ \text{m/s}$, its wavelength is approximately $\frac{340\ \text{m/s}}{500\ \text{Hz}}=0.68\ \text{m}$.

Takeaway: The source sets frequency; the medium affects the speed of sound and, in turn, its wavelength.

Sound, hearing, and pitch

Humans typically hear frequencies from about $20\ \text{Hz}$ to $20{,}000\ \text{Hz}$, although the range varies among individuals and often narrows with age. Lower frequency is heard as lower pitch, while higher frequency is heard as higher pitch. Sound intensity is power per unit area, and sound level is commonly expressed in decibels (dB), a logarithmic scale. Pitch and loudness are perceptual qualities: perceived loudness also depends on frequency and on the listener.

Sound moves through the hearing system in stages:

1. The outer ear collects sound and directs it through the ear canal to the eardrum.

2. Eardrum vibrations move the three middle-ear bones: the malleus, incus, and stapes.

3. The bones transmit vibration to fluid in the cochlea.

4. A traveling wave along the basilar membrane bends sensory hair-cell stereocilia.

5. This triggers electrical signals that travel along the auditory nerve to the brain.

Different regions of the cochlea respond most strongly to different frequencies, supporting pitch discrimination. In this way, mechanical vibrations are transformed into neural signals.

Ultrasound imaging and echoes

Ultrasound is sound above the upper limit of human hearing, about $20\ \text{kHz}$. Diagnostic ultrasound typically uses much higher frequencies, commonly in the megahertz range. A probe, or transducer, converts electrical pulses into sound and returning echoes into electrical signals. Coupling gel removes the air gap between probe and skin; without it, much of the sound would reflect at the boundary.

When sound reaches a boundary between tissues, some reflects and some continues onward. The amount of reflection depends in part on the difference in acoustic impedance between the tissues. A scanner estimates the depth of a reflecting structure from the echo’s round-trip travel time:

Here, $d$ is depth, $v$ is the assumed speed of sound in tissue, and $t$ is the time between sending a pulse and receiving its echo. The factor of $2$ accounts for the outward and return paths.

Example: If the assumed tissue sound speed is $1540\ \text{m/s}$ and an echo returns after $40\ \mu\text{s}$, the estimated depth is about $3.1\ \text{cm}$.

Higher-frequency ultrasound can show finer detail, but it is attenuated more strongly and does not penetrate as deeply. Lower frequencies are useful for deeper structures, with less detail. Probe and setting choices therefore balance image detail against penetration.

Applications and prudent use

Ultrasound is used for fetal and abdominal imaging, echocardiography, and guidance during needle procedures or biopsies. Doppler ultrasound uses changes in the frequency of echoes from moving blood cells to assess blood flow.

Ultrasound images are produced in real time and do not use ionizing radiation. However, ultrasound deposits energy in tissue and can cause heating and mechanical effects. Its use should be clinically appropriate and limited to what is needed for the examination.

Key connection: Ordinary ultrasound imaging uses reflected pulses to locate tissue boundaries, while Doppler ultrasound uses echo-frequency changes to assess motion, including blood flow.