Describing Sound Waves

Chapter 3 Describing Sound Waves

1. Parameters of a Sound Wave

  • Seven key parameters describe sound waves.

2. Ultrasound System

  • The ultrasound system and transducer serve as the sound wave’s source.

3. Period

  • Definition: The time it takes a wave to vibrate a single cycle; the time from the start of one cycle to the start of the next cycle.

  • Units: Microseconds (µs)

  • Typical Values: 0.06 to 0.5 µs

  • Determined by: Sound source only.

  • Adjustable: No.

4. Frequency

  • Definition: The number of particular events occurring in a specific duration of time; specifically, the number of cycles occurring in one second.

  • Units: Hertz (Hz), where 1 Hz = 1 cycle/second.

  • Typical Values: 2 MHz to 15 MHz.

  • Determined by: Sound source only.

  • Adjustable: No.

5. Relationship Between Frequency and Period

  • a. Frequency and period are inversely related and reciprocal.

  • b. Formula: extPeriodimesextFrequency=1ext{Period} imes ext{Frequency} = 1

6. Frequency Ranges

  • Infrasound: less than 20 Hz.

  • Audible Sound: between 20 Hz and 20 kHz (20,000 Hz).

  • Ultrasound: greater than 20 kHz (20,000 Hz).

7. Bigness Parameters

  • Three bigness parameters include:

    • Amplitude

    • Power

    • Intensity

8. Amplitude

  • Definition: The “bigness” of a wave; measured as:

    • The difference between the maximum value and the average or undisturbed value of an acoustic variable.

    • The difference between the minimum value and the average value of an acoustic variable (peak-to-peak amplitude).

  • Units: Decibels (dB)

  • Typical Values: From 1 million pascals (1 MPa) to 3 million pascals (3 MPa).

  • Determined by: Sound source only.

  • Adjustable: Yes.

9. Power

  • Definition: The rate of energy transfer or the rate at which work is performed; describes the “bigness” of a wave.

  • Units: Watts (W)

  • Typical Values: 0.004 to 0.90 watts (4 to 9 milliwatts).

  • Determined by: Sound source only.

  • Power decreases as sound propagates through the body; the rate of decrease depends on the characteristics of the medium and wave.

  • Adjustable: Yes.

10. Intensity

  • Definition: The concentration of energy in a sound beam; describes the “bigness” of a wave.

  • Units: Watts per square centimeter (W/cm²)

  • Typical Values: 0.01 to 300 W/cm².

  • Determined by: Sound source only.

  • Adjustable: Yes.

11. Relationships Among Power, Amplitude, and Intensity

  • a. Relationship: Power, amplitude, and intensity are directly related; all describe the magnitude or strength of a wave.

  • b. Formulas demonstrating their relationships:

    • extPowerriangleqextAmplitude2ext{Power} riangleq ext{Amplitude}^2

    • extIntensityriangleqextAmplitude2ext{Intensity} riangleq ext{Amplitude}^2

    • extIntensityriangleqextPowerext{Intensity} riangleq ext{Power}

    • extIntensity(W/cm2)=racextPower(W)extArea(cm2)ext{Intensity (W/cm²)} = rac{ ext{Power (W)}}{ ext{Area (cm²)}}

  • c. Power, amplitude, and intensity are unrelated to frequency and unrelated to propagation speed. All three parameters decrease as sound travels deeper into the body due to attenuation.

12. Wavelength

  • Definition: The distance or length of one complete cycle.

  • Units: millimeters (mm), meters (m).

  • Typical Values: 0.1 to 0.8 mm.

  • Determined by: Both the source and medium.

  • Adjustable: No.

13. Relationship of Wavelength to Frequency

  • a. Wavelength and frequency are inversely related: as frequency increases, wavelength decreases.

    • Effect of Frequency: Lower frequency results in longer wavelength (leading to decreased resolution and more penetration). Higher frequency results in shorter wavelength (leading to better resolution and less penetration).

  • b. Formula for the relationship:

    • extWavelength(extlext)=raccfext{Wavelength (} ext{l} ext{)} = rac{c}{f}

    • Where cc is the propagation speed, ff is frequency.

14. Relationship of Wavelength to Propagation Speed

  • c. Wavelength is directly proportional to propagation speed/acoustic velocity.

15. Propagation Speed

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

  • Units: Meters per second (m/s), millimeters per microsecond (mm/µs), any distance divided by time.

  • Typical Values: 500 m/s to 4000 m/s.

  • Determined by: The medium.

  • Adjustable: No.

16. Average Speed of Sound in Soft Tissue

  • The average speed of sound in soft tissue is approximately:

    • 1540 m/s, 1.54 mm/µs, or 1.54 km/s (approximately 1 mile per second).

17. Speed Rankings in Different Media

  • List from fastest to slowest:

    • Bone > Muscle > Blood > Soft Tissue > Fat > Lung.

18. Medium Characteristics Influencing Speed

  • a. Two characteristics of the medium that determine speed:

    • Stiffness (also known as bulk modulus)

    • Density

  • b. Most Important Factor: Stiffness, as it has the greatest influence on speed.

  • c. Speed Changes:

    • Speed increases when stiffness increases.

    • Speed decreases when stiffness decreases.

    • Speed increases when compressibility decreases.

    • Speed increases when elasticity increases.

    • Speed decreases when density increases.

    • Speed increases when density decreases.

19. Opposite Terms to Stiffness

  • Two terms that mean the opposite of stiffness are:

    • Elasticity

    • Compressibility