Describing Sound Waves

Seven parameters completely characterize a sound wave: Period, Frequency, Amplitude, Power, Intensity, Wavelength, and Speed.
Each parameter has specific units, can be determined by the sound source or the medium, and may or may not be adjustable by the sonographer.

Definition: The time it takes a wave to vibrate a single cycle.
Units: Seconds, microseconds (\mu s), hours, days.
Typical Values (Diagnostic Ultrasound): 0.06 to 0.5 \mu s (6 \times 10^{-8} to 5 \times 10^{-7} seconds).
Determined By: Sound source only.
Adjustable: No.

Definition: The number of cycles that occur in one second.
Units: Per second, Hertz (Hz), kilohertz (kHz), megahertz (MHz). (1 Hz = 1 cycle/second).
Typical Values (Clinical Imaging): 2 MHz to 15 MHz.
Determined By: Sound source only.
Adjustable: No.
Sound Classification:
- Infrasound: Frequencies less than 20 Hz (inaudible).
- Audible Sound: Frequencies between 20 Hz and 20,000 Hz (20 kHz).
- Ultrasound: Frequencies greater than 20,000 Hz (20 kHz) (inaudible).
Relationship with Period: Inversely related and reciprocal. Period \times Frequency = 1.

These three parameters describe the size, magnitude, or strength of a sound wave. They are generally directly related.

Definition: The difference between the maximum value and the average value of an acoustic variable.
Units: Pascals (pressure), g/cm^3 (density), cm (particle motion), decibels (dB) (relative).
Typical Values (Pressure Amplitude): 1 MPa to 3 MPa.
Determined By: Initially by the sound source, then decreases as sound propagates.
Adjustable: Yes (initial amplitude).
Peak-to-Peak Amplitude: The difference between maximum and minimum values, which is twice the amplitude.

Definition: The rate of energy transfer or the rate at which work is performed.
Units: Watts.
Typical Values (Clinical Imaging): 0.004 to 0.090 watts (4 to 90 milliwatts).
Determined By: Initially by the sound source, then decreases as sound propagates.
Adjustable: Yes (initial power).
Relationship with Amplitude: Power is proportional to the wave's amplitude squared (power \propto amplitude^2).

Definition: The concentration of energy in a sound beam; calculated as power divided by the beam's cross-sectional area. Intensity (W/cm^2) = Power (W) / Area (cm^2)
Units: Watts/square centimeter (W/cm^2).
Typical Values (Clinical Imaging): 0.01 to 300 W/cm^2.
Determined By: Initially by the sound source, then changes as sound propagates.
Adjustable: Yes (initial intensity).
Relationship with Power: Intensity is proportional to power (intensity \propto power).
Relationship with Amplitude: Intensity is proportional to the wave's amplitude squared (intensity \propto amplitude^2).

Definition: The distance or length of one complete cycle.
Units: Millimeters (mm), meters, or any unit of length.
Typical Values (Soft Tissue): 0.1 to 0.8 mm.
Determined By: Both the sound source and the medium (unique).
Adjustable: No.
Relationship with Frequency (in soft tissue): Inversely related. Wavelength (mm) = \frac{1.54 mm/\mu s}{Frequency (MHz)}.
Importance: Shorter wavelengths typically lead to higher quality images with greater detail, produced by high-frequency sound.

Definition: The rate at which a sound wave travels through a medium.
Units: Meters per second (m/s), mm/\mu s, kilometers per second (km/s).
Typical Values (Body): 500 m/s to 4000 m/s.
Typical Values (Soft Tissue, average): 1,540 m/s (1.54 mm/\mu s or 1.54 km/s).
Determined By: Only by the medium through which the sound is traveling (unique). Speed is unaffected by the sound wave's frequency.
Adjustable: No.
Equation: Speed (m/s) = Frequency (Hz) \times Wavelength (m).
Factors Affecting Speed:
- Stiffness (Bulk Modulus): Directly related; as stiffness increases, speed increases.
- Density: Inversely related; as density increases, speed decreases.
- Stiffness has the greatest influence on speed.
General Rule: Sound travels fastest in solids, slower in liquids, and slowest in gases.