Import Question JSON

Current Question (ID: 16014)

Question:

$\text{If we study the vibration of a pipe open at both ends, then which of the following statements is not true:}$

Options:

1. $\text{Odd harmonics of the fundamental frequency will be generated.}$
2. $\text{All harmonics of the fundamental frequency will be generated.}$
3. $\text{Pressure change will be maximum at both ends.}$
4. $\text{The open end will be an antinode.}$

Solution:

$\text{Hint: } f_0 = \frac{nv}{2l}$ $\text{Step: Analyse each option one by one.}$ $\lambda_1 = 2l$ $f : 2f : 3f : 4f : 5f \ldots \left[ f = \frac{v}{2l} \right]$ $\text{Therefore, in the open organ pipe both odd and even harmonics will present.}$ $\text{When air is blown into the open organ pipe. Then, the antinodes are formed at the ends and a node is formed in the middle of the pipe.}$ $\text{So, options (a), (b), and (d) are correct.}$ $\text{And pressure change is minimum at the antinode.}$ $\text{Hence, option (3) is the correct answer.}$

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
}