Production And Use Of Ultrasound (Copy)

Piezoelectric Effect and Ultrasound Transducers

• Piezoelectric Effect:
  • A piezoelectric crystal deforms (changes shape) when a potential difference (p.d.) is applied across it.
  • Conversely, when the shape of the crystal changes (e.g. due to pressure from sound waves), it generates an electromotive force (e.m.f.).
  • Example crystals: quartz, lead zirconate titanate (PZT).
• Ultrasound Transducer:
  • Acts as both generator and detector of ultrasound.
  • Generation: An alternating voltage across the crystal makes it vibrate, producing ultrasound waves.
  • Detection: Incoming ultrasound causes the crystal to compress/expand, producing a measurable voltage.

Diagnostic Use of Ultrasound

• Pulse-Echo Method:
  • A pulse of ultrasound is sent into the body.
  • It reflects at boundaries between materials with different acoustic impedances.
  • Reflected signals (echoes) are detected and used to reconstruct an image or measure depth.
• Applications:
  • Imaging of soft tissues (e.g. liver, kidneys, fetus in womb).
  • Detecting cysts, tumors, or organ abnormalities.

Specific Acoustic Impedance

• Definition:
  Z = ρc
  • Z = specific acoustic impedance (kg m⁻² s⁻¹)
  • ρ = density of the medium (kg m⁻³)
  • c = speed of sound in the medium (m s⁻¹)
• Explanation:
  • A measure of how much resistance a medium offers to the passage of ultrasound.
  • Determines the proportion of ultrasound that is reflected or transmitted at a boundary.

Intensity Reflection Coefficient

• Formula:
  Iᴿ / I₀ = (Z₁ − Z₂)² / (Z₁ + Z₂)²
  • Iᴿ = intensity of reflected wave
  • I₀ = intensity of incident wave
  • Z₁, Z₂ = specific acoustic impedances of two media
• Interpretation:
  • Larger difference in impedance → higher reflection.
  • If Z₁ = Z₂, then no reflection, wave passes completely.
• Example:
  • Ultrasound from muscle (Z₁) to bone (Z₂): high reflection due to large impedance difference.

Attenuation of Ultrasound in Matter

• Formula:
  I = I₀e⁻ᵘˣ
  • I = intensity at distance x
  • I₀ = initial intensity
  • μ = attenuation (absorption) coefficient (m⁻¹)
  • x = depth or thickness of tissue (m)
• Explanation:
  • Intensity decreases exponentially as ultrasound passes through material.
  • Due to absorption, scattering, and reflection.
• Implication:
  • Limits the penetration depth of ultrasound in dense tissues.
  • May require signal amplification or frequency adjustment for deep imaging.

Graphical Representation

• I vs x graph:
  • Exponential decay curve
  • Shape matches I = I₀e⁻ᵘˣ
• Iᴿ/I₀ vs Z₁–Z₂:
  • Reflects increasing return signal with greater mismatch

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course