Math Problem Statement

T4 Wave.pdf

202.97 KB

Solution

The document provides details of tutorial exercises on topics involving waves, refraction, and structural forms. Below are the exercises and a summary of their requirements:

Questions in the Document:

  1. Refraction of Light Across Media:

    • A light ray transitions through gas, liquid, and plastic mediums.
    • Tasks include:
      • Calculating angles AA, BB, and CC.
      • Determining the wavelength of the light in the liquid.
      • Calculating the velocity of light in plastic.
  2. Wave Motion Analysis:

    • Based on a given figure:
      • Determine the amplitude, period, frequency, and velocity.
  3. Structural Elements and Forms:

    • Explanation required for:
      • Tie rods, beams, and columns.
      • Considerations in choosing structural forms.
  4. Refraction of Red Light Through a Prism:

    • Calculations involving:
      • Refractive index of glass.
      • Frequency of light in air.
      • Wavelength and speed of light in glass.
      • Emitting angle (rrr_r).

The document also includes example answers for the calculations and explanations, with the solutions given as:

  • A=33.1A = 33.1^\circ, B=19.96B = 19.96^\circ, C=55C = 55^\circ
  • Wavelength in liquid: 4×107m4 \times 10^{-7} \, \text{m}
  • Velocity in plastic: 1.56×108m/s1.56 \times 10^8 \, \text{m/s}
  • For red light:
    • Refractive index (nn) of glass: 1.35721.3572
    • Frequency in air: 4.29×1014Hz4.29 \times 10^{14} \, \text{Hz}
    • Wavelength in glass: 5.16×107m5.16 \times 10^{-7} \, \text{m}
    • Speed in glass: 2.21×108m/s2.21 \times 10^8 \, \text{m/s}
    • Emitting angle: 60.760.7^\circ

Let me know which question you want to explore further or need help solving!


Would you like a detailed explanation or solution for any specific part?

Related Questions:

  1. What is Snell's Law and how does it apply to calculating refractive angles?
  2. How are period and frequency related in wave motion?
  3. What are the roles of structural elements like tie rods, beams, and columns in construction?
  4. How does the refractive index affect the speed and wavelength of light in different media?
  5. What is the significance of understanding wave motion in practical applications like engineering or physics?

Tip: When solving refraction problems, always ensure you understand the relationship between refractive indices, angles, and

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Math Problem Analysis

Mathematical Concepts

Refraction of light
Wave motion analysis
Geometrical optics
Structural analysis

Formulas

Snell's Law: n1 * sin(θ1) = n2 * sin(θ2)
Wave velocity: v = f * λ
Refractive index: n = c/v

Theorems

Snell's Law for refraction
Wave equations

Suitable Grade Level

Grades 11-12