Import Question JSON

Current Question (ID: 16039)

Question:

$\text{Three sound waves of equal amplitudes have frequencies of } (n - 1), n, \text{ and } (n + 1).$ $\text{They superimpose to give beats. The number of beats produced per second will be:}$

Options:

1. $1$
2. $4$
3. $3$
4. $2$

Solution:

$\text{Hint: Beat frequency per second } = |n_1 - n_2|$ $\text{Step: Find the beat frequency of the sound wave.}$ $\text{Beats produced is the maximum difference between two wave frequency}$ $\text{Beat frequency} = f_1 \sim f_2 = n - (n - 1) = 1 \text{ and similarly for } n \text{ and } n + 1$ $\text{Beat frequency} = (n + 1) - (n - 1) = 2$ $\text{The beat frequency of the sound wave is 2.}$ $\text{Hence, option (4) is the correct answer.}$

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
}