Sound Wave Parameters

Describing Sound Waves

Introduction

• Sound waves are characterized by seven parameters.

  • Importance of understanding both the meaning and the units of these parameters.

  • Parameters include:

  • Period

  • Frequency

  • Amplitude

  • Power

  • Intensity

  • Wavelength

  • Speed

Understanding Ultrasound Physics

• Distinction between parameters determined by the sound source and those determined by the medium.

• The ultrasound system and transducer establish levels of some parameters, while tissue (the medium) defines others.

• Importance of knowing typical values for clinical medicine and ultrasound physics:

  • Typical Values are useful for accurate diagnostics.

Parameters of Sound Waves

Period

• Definition: The time taken for one wave cycle, from the start of one cycle to the start of the next cycle.

• Units: Reported in time units such as microseconds ( ext{μs}), seconds, hours, or days.

• Typical Values: Ranges from 0.06 to 0.5 ext{μs}, equivalent to 6 imes 10^{-8} to 5 imes 10^{-7} seconds.

• Determined By: The sound source only; not by the medium.

• Adjustable: No; the sonographer cannot change the period with a basic ultrasound system.

Frequency

• Definition: Number of cycles occurring within a specific time period, specifically one second in diagnostic ultrasound.

  • For context, presidential elections occur:

  • 25 times per century

  • 2.5 times per decade

  • Every four years.

• Units: Reported in Hertz (Hz), where:

  • 1 ext{ cycle/second} = 1 ext{ Hz}

  • 1,000 ext{ cycles/second} = 1 ext{ kHz}

  • 1,000,000 ext{ cycles/second} = 1 ext{ MHz}

• Typical Values: In diagnostic imaging, ranges from approximately 2 MHz to 15 MHz.

• Determined By: The sound source only; not the medium.

• Adjustable: No; the sonographer cannot alter the frequency with a basic system.

More About Frequency

• Classification of Sound:

  • Frequencies below 20 Hz: Infrasonic (inaudible).

  • Frequencies from 20 Hz to 20,000 Hz: Audible Sound.

  • Frequencies above 20,000 Hz: Ultrasonic (ultrasound).

• Impact on Diagnostic Sonography: Affects penetration and image quality.

• Relationship Between Frequency and Period: Inversely related.

  • As frequency increases, period decreases, and vice versa.

  • Reciprocal relationship: ext{Period} imes ext{Frequency} = 1

More about Hertz

• Clarification of the meaning of Hertz:

  1. Represents events per second.

  2. Context of 'event' matters (e.g., cycles for sound waves).

• Example in various contexts:

  • Sound wave at 100 Hz = 100 cycles per second.

  • TV frame rate at 120 Hz = 120 frames per second.

  • Heart rate at 1 Hz = 60 beats per minute.

Three "Bigness" Parameters

• Describes size or strength of sound waves:

  1. Amplitude

  2. Power

  3. Intensity

Amplitude

• Definition: The bigness of a wave, calculated as the difference between the maximum value and the average value of an acoustic variable.

• Units: Can be in pascals for pressure, cm for particle motion, etc.; sometimes expressed in decibels (dB).

• Typical Values: In clinical imaging, ranges from 1 MPa to 3 MPa.

• Determined By: Initially by the sound source, but decreases as it travels through the body.

• Adjustable: Yes; can be altered by the sonographer.

More About Amplitude

• Difference Between Amplitude and Peak-to-Peak Amplitude:

  • Amplitude measures from middle/average value to the maximum value.

  • Peak-to-Peak amplitude is twice the amplitude (measures from maximum to minimum).

Power

• Definition: The rate of energy transfer or rate of work performed by the wave, describing the wave’s bigness.

• Units: Measured in watts.

• Typical Values: In clinical imaging, ranges from 0.004 to 0.090 watts (4 - 90 mW).

• Determined By: Initially by sound source and decreases with propagation.

• Adjustable: Yes; can be changed by the sonographer.

• Relationship with Amplitude: Power is proportional to the square of amplitude (P ext{ is proportional to } A^2).

Examples of Power Relationship

• If amplitude increases by a factor of 3, power increases by a factor of 9 (3 imes 3 = 9).

• If amplitude decreases to half, power decreases to a quarter (25%) of its original value (0.5^2 = 0.25).

Intensity

• Definition: Concentration of energy in a sound beam, calculated as power divided by the beam's cross-sectional area (I = rac{P}{A}).

• Units: Measured in watts/cm².

• Typical Values: In clinical imaging, ranges from 0.01 to 300 W/cm².

• Determined By: Initially by sound source and changes with propagation.

• Adjustable: Yes; can be changed by the sonographer.

More About Intensity

• Intensity Relationships: Intensity is directly proportional to power and proportional to amplitude squared.

  • If power doubles, intensity doubles.

  • If amplitude doubles, intensity increases fourfold (2 imes 2 = 4).

Wavelength

• Definition: The distance or length of one complete cycle in a sound wave.

• Units: Measured in mm or meters.

• Typical Values: In soft tissue, ranges from 0.1 mm to 0.8 mm.

• Determined By: Both sound source and medium.

• Adjustable: No; sonographer cannot change wavelength.

More About Wavelength

• Difference Between Wavelength and Period: Wavelength refers to distance, while period refers to time.

• Relationship with Frequency: Inversely related; as frequency increases, wavelength decreases.

• Example: Frequency of 1 MHz results in a wavelength of 1.54 mm in soft tissue.

• To calculate wavelength: ext{Wavelength (mm)} = rac{1.54 ext{ mm}}{ ext{Frequency (MHz)}}

• Shorter wavelengths produce higher quality images; higher frequency transducers preferred for better imaging.

Speed

• Definition: Rate at which sound wave travels through a medium.

• Units: Measured in meters/second or mm/us.

• Typical Values: In body, speed ranges from 500 m/s to 4000 m/s depending on the tissue.

• Determined By: Only by the medium, not affected by sound wave characteristics.

• Adjustable: No; speed changes only with a change of medium.

More About Speed

• Speed in Soft Tissue: Average speed is 1,540 m/s, also reported as 1.54 mm/us.

• Speed in Various Media:

  • Air: 330 m/s

  • Water: 1,480 m/s

  • Bone: 3,500 m/s

• Characteristics Affecting Speed:

  1. Stiffness: Directly related to speed; as stiffness increases, speed increases.

  2. Density: Inversely related to speed; as density increases, speed decreases.

Summary of Sound Wave Parameters

• Organization of parameters:

  • Five parameters determined initially by the sound source (Period, Frequency, Amplitude, Power, Intensity).

  • The parameters related to size include Amplitude, Power, and Intensity.

  • Wavelength is uniquely determined by both source and medium.

  • Speed is solely determined by the medium.

  • Period and Frequency are reciprocals.