Import Question JSON

Current Question (ID: 16028)

Question:

$\text{A student tunes his guitar by striking a } 120 \text{ Hz with a tuning fork and playing the } 4^{\text{th}} \text{ string at the same time. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which of the following frequencies is most likely the frequency of the } 4^{\text{th}} \text{ string on his guitar?}$

Options:

1. $130$
2. $117$
3. $110$
4. $120$

Solution:

$\text{Hint: beat frequency per second } = |f_1 - f_2|$ $\text{Step: Find the possible frequency of the 4th string on the string.}$ $\text{The beat frequency, } f = 3 \text{ Hz}$ $\text{The possible frequencies of the 4th string,}$ $f_1 = 3 + 120 = 123 \text{ Hz}$ $f_2 = 120 - 3 = 117 \text{ Hz}$ $\text{Therefore, the possible frequencies of the 4th string on the string are 123 and 117 Hz.}$ $\text{Hence, option (2) is the correct answer.}$

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
}