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.