5.3 Frequency, Bandwidth, Q Factor, Power, Pressure, Intensity & Amplitude

Frequency and Bandwidth

Frequency is the number of cycles a wave completes per second, in hertz (Hz) or megahertz (MHz); diagnostic imaging uses roughly 2 to 15 MHz. The operating frequency of a pulsed transducer is set by the thickness of the piezoelectric element — the element resonates most efficiently when its thickness equals one-half wavelength of sound within the crystal material. Frequency is determined by the source, not the medium: it does not change as sound propagates through tissue, even though wavelength and speed can.

A real imaging pulse is never a single pure frequency. Bandwidth is the range of frequencies present in the pulse, from the lowest to the highest meaningful component; the center of that range is the resonant (center) frequency. The shorter and more heavily damped a pulse is, the broader its bandwidth. Broadband pulses are desirable for imaging because a short pulse gives a short spatial pulse length and therefore good axial resolution; the spread of frequencies also supports harmonic imaging and frequency-compounding techniques.

Q Factor

The quality factor (Q factor) ties these ideas together:

• Q = center frequency / bandwidth (unitless)

A low Q factor means a broad bandwidth relative to the center frequency — the hallmark of a short, heavily damped imaging pulse. Imaging transducers are deliberately built as low-Q devices. A high Q factor means a narrow bandwidth and a long, "ringing" pulse, which is exactly what continuous wave Doppler crystals produce — they are high-Q because damping would only reduce their sensitivity. Exam pairings to memorize: imaging probe = low Q, broad bandwidth, short pulse; CW Doppler = high Q, narrow bandwidth, long pulse.

Amplitude, Pressure, and Power

Amplitude is the maximum variation of an acoustic variable from its undisturbed baseline — how "big" the wave is. When the measured variable is pressure, amplitude is expressed as pressure in megapascals (MPa); the peak rarefactional pressure of a pulse is used in calculating the mechanical index.

Power is the rate at which energy is transferred, in watts (W) or milliwatts (mW). Power is proportional to amplitude squared:

• Power ∝ amplitude²

Worked example: if the amplitude of a beam doubles, its power increases by 2² = four times; if amplitude is halved, power falls to one-quarter. This squared relationship is a guaranteed exam calculation. Both amplitude and power decrease continuously as the beam attenuates in tissue, and both are zero during the listening portion of the PRP.

Intensity and Its Six Variants

Intensity is the beam's power spread over the cross-sectional area it occupies:

• Intensity = power / area, in watts per square centimeter (W/cm²) or mW/cm²

Because a beam is stronger at its center than at its edges, and because a pulsed beam is "on" only briefly, intensity must be specified in space and time. Space gives two choices — spatial peak (SP), the highest value within the beam, versus spatial average (SA), the mean across the whole beam. Time gives three — temporal peak (TP), the value at the instant of maximum output; pulse average (PA), averaged over the pulse duration; and temporal average (TA), averaged over the entire pulse repetition period, including listening time. Combined, these yield six variants:

The exam's favorite fact: SPTA is the intensity most relevant to bioeffects because tissue heating depends on energy delivered over time, and temporal averaging captures the low duty factor of pulsed imaging. SPTP is the largest value and SATA the smallest for any given beam. The variants are linked by the duty factor: temporal average = pulse average × duty factor (so with a duty factor of 0.3%, SPTA is only 0.003 times SPPA). Typical diagnostic values range from a few mW/cm² (SATA) to several hundred mW/cm² for SPTA in Doppler modes, while SPTP can reach tens of W/cm² or more. Output display standards (mechanical index and thermal index) exist precisely so the sonographer can follow the ALARA principle — as low as reasonably achievable — while working with these quantities.

Worked Intensity Examples

Example 1: a beam carries 20 mW of power distributed over a 2 cm² area. Its spatial average intensity is 20 mW / 2 cm² = 10 mW/cm². If the spatial peak is twice the spatial average (a common exam assumption), the spatial peak value is 20 mW/cm².

Example 2: a pulsed beam has an SPPA of 40 W/cm² and a duty factor of 0.002 (0.2%). Its SPTA = 40 W/cm² × 0.002 = 0.08 W/cm² = 80 mW/cm². This is why pulsed imaging, despite enormous instantaneous peak intensities, delivers modest average energy — and why continuous wave Doppler, with a duty factor of 1, has equal pulse-average and temporal-average intensities.

Finally, note that intensity, power, and amplitude all decrease as the beam travels deeper because of attenuation (absorption, reflection, and scatter), and all three are directly adjustable from the console via the output power (transmit) control — unlike frequency or spatial pulse length, which are fixed by the transducer.