Sound Waves, Units and Pulse Parameters · 8 min read
The Seven Acoustic Parameters
This chapter defines the seven parameters that describe a sound wave, gives their units and typical values, and, most importantly for the exam, states what determines each one and whether the sonographer can change it.
Period and Frequency
Period is the time it takes to complete one cycle. Its unit is time; in diagnostic ultrasound the period is very short, typically 0.06 to 0.5 µs.
Frequency is the number of cycles that occur in one second, measured in hertz. One hertz is one cycle per second; 1 MHz is 1 million cycles per second.
Period and frequency are reciprocals: period = 1 / frequency, and period × frequency = 1. When frequency goes up, period goes down by the same factor. A handy unit pairing is that period in µs = 1 / frequency in MHz.
Worked example 1, period of a 5 MHz wave:
Period (µs) = 1 / frequency (MHz). Period = 1 / 5 = 0.2 µs.
Worked example 2, period of a 2 MHz wave: Period = 1 / 2 = 0.5 µs.
Halving the frequency from 4 MHz (period 0.25 µs) to 2 MHz doubles the period from 0.25 µs to 0.5 µs, which confirms the inverse relationship.
Worked example 3, frequency from period: a wave has a period of 0.1 µs. Frequency = 1 / 0.1 = 10 MHz.
Both period and frequency are determined by the sound source, meaning the transducer and the machine that drives it. The medium does not change them, and the sonographer cannot adjust them with a knob on the same transducer except by selecting a different transducer or a different operating frequency on a broadband probe (which is really choosing a different source frequency).
Scanning Scenario: A sonographer scanning a slim patient's thyroid switches from a 7 MHz setting to a 12 MHz setting on a broadband linear probe. The frequency rises and the period falls (from about 0.14 µs to about 0.08 µs). The image gains detail, but penetration drops, a trade-off explained in Section 2.
Amplitude, Power and Intensity
These three parameters describe the strength, or "bigness," of the wave.
Amplitude is the maximum change in an acoustic variable from its resting (average) value. It is measured from the middle of the wave to the peak, not from peak to trough. Units are those of the variable: pascals for pressure, kg/cm³ for density, or cm for distance. Peak-to-peak amplitude is twice the amplitude.
Power is the rate at which energy is transferred, measured in watts (W) or milliwatts (mW). Power is proportional to amplitude squared (power ∝ amplitude²).
Intensity is power concentrated in an area: intensity = power / beam area, measured in W/cm² or mW/cm². Because intensity depends on power, intensity is also proportional to amplitude squared.
All three are determined by the sound source, and all three decrease as sound travels through tissue (attenuation, covered in Section 2). Unlike period and frequency, the sonographer can change them directly with the output power control (also called transmit power, acoustic power or energy output). Raising output power raises amplitude, power and intensity, which brightens every echo on the image and increases patient exposure.
Worked example 1, intensity from power and area: a beam carries 2 W over an area of 4 cm².
Intensity = power / area. Intensity = 2 W / 4 cm² = 0.5 W/cm².
Worked example 2, the same power focused into a smaller area: 30 mW over 0.5 cm². Intensity = 30 mW / 0.5 cm² = 60 mW/cm².
If focusing narrows the beam area to 0.25 cm² with the same 30 mW, intensity = 30 / 0.25 = 120 mW/cm². Halving the area doubles the intensity. This is why focusing raises intensity at the focus even though output power is unchanged.
Worked example 3, amplitude changes: the amplitude doubles.
Power ∝ amplitude², so the new power = 2² = 4 times the original.
Intensity is also ∝ amplitude², so intensity rises 4 times as well.
Worked example 4, amplitude halves: power and intensity become (1/2)² = 1/4 of their original values. If the amplitude triples, power and intensity rise 3² = 9 times.
Amplitude, Power and Intensity Relationships
| Change | Power | Intensity |
|---|---|---|
| Amplitude doubled | ×4 | ×4 |
| Amplitude halved | ×1/4 | ×1/4 |
| Power doubled, same area | ×2 | ×2 |
| Beam area halved, same power | unchanged | ×2 |
Common Trap: When amplitude doubles, students often say intensity doubles. It quadruples, because intensity depends on amplitude squared. When power doubles, intensity doubles, because intensity is directly proportional to power.
Wavelength
Wavelength is the length of one complete cycle, the distance from one compression to the next. Its units are length; in soft tissue at imaging frequencies it is about 0.1 to 0.8 mm.
Wavelength is the only parameter determined by both the source and the medium. The source sets the frequency, and the medium sets the speed, and wavelength = propagation speed / frequency. In soft tissue, speed is 1.54 mm/µs, which gives a very useful shortcut: wavelength (mm) = 1.54 / frequency (MHz).
Worked example 1, 5 MHz in soft tissue:
Wavelength (mm) = 1.54 / frequency (MHz).
Worked example 2, 2 MHz in soft tissue: Wavelength = 1.54 / 2 = 0.77 mm.
Worked example 3, 10 MHz in soft tissue:
Doubling frequency from 5 to 10 MHz halves the wavelength from 0.31 to 0.15 mm. Frequency and wavelength are inversely related in a given medium.
Worked example 4, wavelength in a different medium: a 2 MHz wave travels in bone at 4 mm/µs (4,000 m/s).
Wavelength = speed / frequency = 4 mm/µs / 2 MHz = 2 mm.
In soft tissue the same 2 MHz wave has a wavelength of 0.77 mm. Same frequency, faster medium, longer wavelength.
Exam Tip: Shorter wavelength produces shorter pulses and better axial (depth) detail, which is the main reason high-frequency transducers produce sharper images. Section 6 turns this into resolution calculations.
Propagation Speed
Propagation speed is how fast sound travels through a medium, in m/s or mm/µs. It is determined only by the medium, specifically by its stiffness and density. Frequency, amplitude and the transducer have no effect on speed. Every frequency travels at the same speed in the same tissue.
Stiffness (also called bulk modulus; its opposite is compressibility) is the resistance of a material to being compressed. Stiffer materials transmit sound faster, so stiffness and speed are directly related. Density, considered alone with stiffness held constant, is inversely related to speed: a heavier, more inert material slows the wave. In real tissues, stiffness differences usually dominate, which is why bone (stiff and dense) is fast and air (very compressible) is slow.
Propagation Speed in Common Media
| Medium | Approximate speed |
|---|---|
| Air | 330 m/s |
| Lung | 500 m/s |
| Fat | 1,450 m/s |
| Soft tissue (average) | 1,540 m/s (1.54 mm/µs) |
| Liver | 1,560 m/s |
| Blood | 1,560 to 1,570 m/s |
| Muscle | 1,600 m/s |
| Bone | 3,500 to 4,080 m/s |
The general order is gases slowest, then liquids, then solids fastest. Within soft tissues the values are close together, which is why the machine can assume a single average of 1,540 m/s. Ultrasound systems assume this speed when they convert echo arrival time into depth. When the real tissue speed differs, reflectors are drawn at the wrong depth (propagation speed error, covered in Section 4).
Summary of What Determines Each Parameter
Who Determines Each Acoustic Parameter
| Parameter | Determined by | Sonographer can change? |
|---|---|---|
| Period | Source | No (only by changing transducer or frequency setting) |
| Frequency | Source | No (only by changing transducer or frequency setting) |
| Amplitude | Source (initially) | Yes, output power |
| Power | Source (initially) | Yes, output power |
| Intensity | Source (initially) | Yes, output power |
| Wavelength | Source and medium | No |
| Propagation speed | Medium only | No |
Memory Aid: "Speed is the medium's; wavelength is shared; the rest belong to the source." Of the source-determined parameters, only the strength trio (amplitude, power, intensity) answers to a knob.
Key Takeaways
Period = 1 / frequency; period (µs) = 1 / frequency (MHz). Both are set by the source.
Amplitude, power and intensity are set by the source, adjustable with output power, and decrease as sound travels.
Power and intensity are proportional to amplitude squared; intensity = power / area.
Wavelength = speed / frequency; in soft tissue, wavelength (mm) = 1.54 / frequency (MHz). It depends on both source and medium.
Propagation speed depends only on the medium: stiffer is faster, denser (alone) is slower; soft tissue averages 1,540 m/s.
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