Import Question JSON

Current Question (ID: 16009)

Question:

$\text{Consecutive frequencies emitted from an organ pipe are } 75 \text{ Hz}, 125 \text{ Hz}, 175 \text{ Hz. The frequency of the tenth overtone will be:}$

Options:

1. $275 \text{ Hz}$
2. $175 \text{ Hz}$
3. $525 \text{ Hz}$
4. $575 \text{ Hz}$

Solution:

$\text{Hint: } f_c = \frac{v}{4l}$ $\text{Step: Find the frequency of the } 10^{\text{th}} \text{ overtone.}$ $\text{The given consecutive frequencies of organ pipe are } 75 \text{ Hz}, 125 \text{ Hz}, 175 \text{ Hz.}$ $\text{Taking the ratios of the frequencies, we get; } 75 : 125 : 175 \Rightarrow 3 : 5 : 7$ $\text{These frequencies are in odd harmonics. Therefore, the organ pipe is closed.}$ $\text{The fundamental frequency of closed organ pipe is } 25 \text{ Hz.}$ $\text{Therefore, the frequency of the } 10^{\text{th}} \text{ overtone =}$ $(2N + 1)f_0 = (2 \times 10 + 1) \times 25 = 21 \times 25 = 525 \text{ Hz}$ $\text{Hence, option (3) is the correct answer.}$

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
}