SaM - Wavelength

Memory Card

---

• IMPORTANTE:
  • $\lambda$ : wavelength, $\left[\lambda \right]=\text{m}$
  • $f$ or $\nu$ : frequency, $\left[f\right]=\text{Hz}$
  • $T=\frac{1}{f}$ : period, $\left[T\right]=s$

---

• For photons, we have seen when talking about photo resisitive sensors:$\lambda =\frac{c}{\nu }$Where:
  • $c=3\cdot 10^8\frac{\text{m}}{\text{s}}$
  • $\nu$ : frequency
• Source: Youtube

---

• For ultrasonic waves:${\lambda }_w=\frac{v_l}{f}$Where:
  • $v_l$ is the longitudinal propagation velocity of the ultrasonic wave.
  • $f$ : frequency

---

• For ultrasonic waves generated by a quartz oscillator:${\lambda }_w\simeq 2t$Where: $t$ is the thickness of the slice of crystal.
• What is the relationship between wavelenght ${\lambda }_w$ and the thikness $t$ of the quartz, for an ultrasonic wave generated by a quartz oscillator? (ChatGPT)
  • The relationship between the wavelength ${\lambda }_w$ and the thickness $t$ of the quartz for an ultrasonic wave generated by a quartz oscillator can be described by the following equation:${\lambda }_w=\frac{2\cdot t}{n}$Where:
    • $lambd{a}_w$ is the wavelength of the ultrasonic wave,
    • $t$ is the thickness of the quartz,
    • $n$ is the refractive index of the quartz.
  • This equation indicates that the wavelength of the ultrasonic wave is directly proportional to the thickness of the quartz and inversely proportional to the refractive index of the quartz.
    So, as the thickness of the quartz increases, the wavelength of the ultrasonic wave also increases, provided the refractive index remains constant.
• Can you explain why this relashiop exists, can you help me understand and visualize? (ChatGPT)
  • Certainly! Let’s break down why this relationship exists and visualize it.
    1. Propagation Speed: Ultrasonic waves propagate through a medium at a certain speed, which is dependent on the properties of the medium. In quartz, this propagation speed is related to the refractive index $n$.
    2. Wavelength: The wavelength of a wave is the distance between two consecutive points that are in phase (e.g., two crests or two troughs). In the context of ultrasonic waves, it’s the distance between two consecutive compression regions or rarefaction regions.
    3. Thickness of Quartz: The thickness of the quartz $t$ determines how far the wave travels through the material before exiting. This distance affects how many wavelengths fit within the quartz material.
  • Visualize this: Imagine an ultrasonic wave entering the quartz material. As it propagates through, it undergoes compression and rarefaction cycles. The distance it travels within the quartz before exiting is the thickness of the quartz. If the quartz is thicker, the wave travels a longer distance before exiting.