Import Question JSON

Current Question (ID: 19970)

Question:

The correct figure that shows, schematically, the wave pattern produced by the superposition of two waves of frequencies $9 \text{ Hz}$ and $11 \text{ Hz}$, is:

Options:

1. Option 1
2. Option 2
3. Option 3
4. Option 4

Solution:

$\text{Hint: Beat frequency} = 2 \text{ Beats/sec}$ $\text{Step: Find the correct wave pattern produced by the superposition of two waves of frequencies } 9 \text{ Hz and } 11 \text{ Hz.}$ $\text{The beat frequency is given by:}$ $f_b = |f_1 - f_2| = |9 - 11| = 2 \text{ Hz}$ $\text{The beat frequency is } 2 \text{ Hz means the two waves are interfering in such a way that the resulting combined wave fluctuates in amplitude at a rate of } 2 \text{ cycles per second.}$ $\text{Therefore, the correct wave pattern showing } f_b = 2 \text{ Hz is shown in the figure below;}$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}