Acoustic Parameters in Physics

Acoustic Parameters

Introduction to Acoustic Parameters

• Acoustic parameters are essential for describing any sound wave.
• There are seven key acoustic parameters:
  1. Period
  2. Frequency
  3. Amplitude
  4. Power
  5. Intensity
  6. Wavelength
  7. Propagation speed

Frequency

• Definition: Number of cycles per second.
• Formula: Number of cycles / seconds
• Unit: Hertz (Hz), 1/second, or per second.
• Determined by: Sound source.
• Adjustable: Sonographers cannot change this value.
• Typical Values: 2 MHz to 20 MHz.
• Sound wave classification based on frequencies:
  • Infrasonic: Frequency < 20 Hz
  • Audible: Frequency between 20 Hz to 20 kHz
  • Ultrasonic: Frequency > 20 kHz
• Frequency is crucial in ultrasound as it affects resolution and penetration.

Period

• Definition: Time it takes for one cycle to occur. It is the reciprocal of frequency.
• Formula: $Period = \frac{1}{Frequency}$ or $Period \times Frequency = 1$
• Unit: Seconds, minutes, or any other unit of time.
• Determined by: Source (US system & transducer).
• Adjustable: Sonographers cannot change this value.
• Typical Values: 0.1 to 0.5 microseconds (µs).

Frequency and Period Relationship

• Inverse relationship exists between frequency and period.
  • If Frequency increases ($F \uparrow$), then Period decreases ($P \downarrow$).
  • If Frequency decreases ($F \downarrow$), then Period increases ($P \uparrow$).
• Examples:
  • If $P = 1$, then $F = \frac{1}{1} = 1$
  • If $P = 2$, then $F = \frac{1}{2}$
    • (If P = double, F = half)
• Always use complementary units with period and frequency (e.g., seconds and hertz, microseconds with megahertz).

"Bigness" Parameters (Strength of Sound Wave)

• These parameters describe the strength of a sound wave:
  1. Amplitude: Maximum variation that occurs in an acoustic variable (Maximum value – normal value).
  2. Power: Rate of energy transfer.
  3. Intensity: Rate at which energy passes through a unit area.

Amplitude

• Definition: Difference between maximum and undisturbed value.
• Unit: Unit of any acoustic variable (Pa, g/cm3, cm, °C).
• Determined by: Sound source.
• Adjustable: Sonographers can change this value.
• Typical Values: 1 MHz to 3 MHz.
• Types of Amplitude:
  • Amplitude: Difference between middle value to maximum value.
  • Peak-to-Peak Amplitude: Difference between minimum value and maximum value.

Power

• Definition: Rate of energy transfer.
• Formula: $power \propto amplitude^2$
• Unit: Watts.
• Determined by: Source (US system & transducer).
• Adjustable: Initial power can be changed.
• Typical Values: 4 to 90 mw (milliwatts).

Intensity

• Definition: Rate at which energy passes through a unit area.
• Formula: $intensity = \frac{power}{area}$
  • $intensity \propto power$
  • $intensity \propto amplitude^2$
• Unit: W/cm\textsuperscript{2}
• Determined by: Source (US system & transducer).
• Adjustable: Initial intensity can be changed.
• Typical Values: 0.01 to 300 W/cm\textsuperscript{2}
• Intensity increases when power and amplitude increase ($Intensity \uparrow$ è power and $amplitude \uparrow$).

Wavelength

• Definition: Distance or length of one complete cycle.
• Formula: $Wavelength = \frac{propagation \ speed}{frequency}$ ($\lambda = \frac{c}{f}$)
• Unit: Any unit of distance (m, mm, cm).
• Determined by: Source & Medium (Only parameter determined by both).
• Adjustable: Sonographers cannot change this value.
• Typical Values: 0.15 to 0.8 mm.

Wavelength and Frequency Relationship

• $\lambda = \frac{c}{f}$
• If $f \uparrow$ è $\lambda \downarrow$ or if $f \downarrow$ è $\lambda \uparrow$
• Frequency is inversely related to wavelength.
• If $C = 1.54$ mm/µs, then $\lambda (mm) = \frac{1.54 \ mm/µs}{f (MHz)}$
• Example:
  • If frequency is 2 MHz, then $\lambda = \frac{1.54}{2} = 0.77$ mm

Propagation Speed

• Definition: Distance traveled by the sound wave in 1 second.
• Formula:
  • $Propagation \ speed (c) = \frac{distance (d)}{time (t)}$
  • $Propagation \ speed (c) = frequency (f) \times wavelength (\lambda)$
• Unit: m/s, mm/µs.
• Determined by: Medium only.
• Adjustable: Sonographer cannot change the speed.
• Typical Values: 500 m/s to 4000 m/s.
• Speed of sound in soft tissue: 1.54 mm/µs or 1540 m/s.

Propagation Speed in Biologic Tissues

• In other media:
  • Air: 330 m/s
  • Water: 1,480 m/s
  • Metal: 2,000 to 7,000 m/s

Factors Affecting Propagation Speed

• Characteristics of the medium that affect the speed of sound:
  1. Stiffness: Object's ability to resist compression.
     • Propagation speed is directly related to stiffness.
     • Stiffness increases ($Stiffness \uparrow$) è Propagation Speed increases ($Propagation \ Speed \uparrow$)
  2. Density: Relative weight of a material.
     • Propagation speed is inversely proportional to the density.
     • Density increases ($Density \uparrow$) à Propagation Speed decreases ($Propagation \ Speed \downarrow$)
• Opposite of stiffness is compressibility and elasticity.

Rarefactions & Compressions

• Compression: When the molecules of the medium are squeezed together.
• Rarefaction: When the molecules of the medium are stretched apart.

Formulas/Units

• Chapter 1:
  • Know conversions
• Chapter 2:
  • $pressure = \frac{Force}{area}$ (Pa, mmHg, N/cm\textsuperscript{2})
  • $density = \frac{mass}{volume}$ (kg/cm\textsuperscript{3})
  • distance (cm, mm, feet, mile)
  • temperature (°C, °F)
• Chapter 3:
  • $Period = \frac{1}{frequency}$ (seconds, minutes)
  • $Frequency = \frac{1}{period}$ (Hz, per second)
  • Amplitude (unit of any acoustic value)
  • $power \propto amplitude^2$ (watts)
  • $Intensity = \frac{power}{area}$, $intensity \propto power$, $intensity \propto amplitude^2$
  • $Wavelength = \frac{propagation \ speed}{frequency}$ (any unit of length)
  • $Propagation \ speed = \frac{distance}{time}$ (m/s, mm/µs)
  • $Stiffness \uparrow$ è Speed $↑$, Density $↑$ è Speed $↓$