Period, Frequency & Wavelength

Frequency: How Many Cycles Per Second

Frequency is the number of complete cycles (one full compression plus one full rarefaction) that occur in one second, measured in hertz (Hz). One hertz equals one cycle per second. Because diagnostic ultrasound frequencies are so high, they are almost always expressed in megahertz (MHz) — one MHz equals one million cycles per second (1,000,000 Hz). Frequency is a source-determined property: it is set by how fast the piezoelectric crystal inside the transducer vibrates (governed largely by crystal thickness, covered in Chapter 5), not by anything in the tissue the sound later travels through. A critical rule to memorize now, because it resurfaces constantly later in the course: frequency does not change as sound passes from one medium into another. A 5 MHz pulse leaving the transducer is still a 5 MHz pulse deep in the liver.

Period: The Reciprocal of Frequency

Period is the time required to complete one full cycle — essentially the "clock" version of frequency. Period and frequency are reciprocals of one another:

Because they are reciprocals, period and frequency always move in opposite directions: as frequency goes up, period goes down, and vice versa. This is a purely mathematical relationship — it holds regardless of what medium the sound is traveling through, because (like frequency) period is fixed by the source and does not change with the medium.

Worked Example

A transducer operating at 5 MHz produces a period of:

Period = 1 / frequency = 1 / 5,000,000 Hz = 0.0000002 seconds = 0.2 microseconds (µs)

Memorize this exact pair (5 MHz ↔ 0.2 µs) — it is one of the most frequently tested numerical relationships on the SPI exam, and the same reciprocal logic applies to any frequency the exam gives you (a 2 MHz transducer produces a 0.5 µs period, a 10 MHz transducer produces a 0.1 µs period, and so on).

Practice: Period at Common Diagnostic Frequencies

The reciprocal relationship holds at every frequency an exam question might use. Practicing the arithmetic at a range of common diagnostic frequencies builds the speed you need for timed testing:

Notice the pattern: as frequency climbs, period keeps shrinking, but the two values never move independently — one is always simply 1 divided by the other, regardless of the medium the sound is currently passing through.

Where Ultrasound Sits on the Frequency Spectrum

"Ultrasound" is simply a name for sound whose frequency is too high for humans to hear:

Notice the enormous gap between the technical definition of ultrasound (anything above 20 kHz) and the frequencies actually used for diagnostic imaging (2–15 MHz, i.e., 2,000,000–15,000,000 Hz). Frequencies barely above 20 kHz are used in industrial and some flow-detection applications, but diagnostic B-mode and Doppler imaging require much higher frequencies than the bare minimum "ultrasound" threshold in order to achieve adequate axial resolution (a relationship explored fully in Chapter 6).

Wavelength: The Spatial Companion to Period

While period and frequency describe the time dimension of a wave cycle, wavelength describes its spatial dimension — the physical distance over which one complete cycle (one compression plus one rarefaction) occurs, typically measured in millimeters. Wavelength is not fixed by the source alone; it also depends on how fast sound is moving through the specific medium it is currently in. Because propagation speed changes tissue-to-tissue while frequency stays constant, wavelength is the variable that changes when sound crosses from one tissue type into another. The full equation linking wavelength, frequency, and propagation speed — and the clinically useful shortcut for calculating wavelength in soft tissue — is covered in the next section (2.3), where you will need today's period/frequency relationship as a foundation.

SPI Exam Tip

Expect the exam to test period/frequency reciprocity in multiple disguises: "what happens to the period if frequency increases?" or a direct calculation ("a 4 MHz transducer produces what period?"). Also expect at least one item testing whether frequency changes with medium — remember, it never does. The only source-independent property that changes when the wave enters a new tissue is propagation speed (and, as a downstream consequence, wavelength). Keep period, frequency, and the reciprocal relationship between them separate in your mind from propagation speed and wavelength, covered next — mixing up which quantities are fixed by the source and which are fixed by the medium is one of the most common ways candidates lose otherwise-easy points on this part of the exam.