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Current Question (ID: 16037)

Question:

$\text{Two vibrating tuning forks produce progressive waves given by}$ $Y_1 = 4 \sin 500\pi t \text{ and } Y_2 = 2 \sin 506\pi t.$ $\text{The number of beats produced per minute is:}$

Options:

1. $3$
2. $360$
3. $180$
4. $60$

Solution:

$\text{Hint: Beat frequency per second} = |\nu_1 - \nu_2|$ $\text{Step: find the beat frequency per minute.}$ $\text{Two progressive waves are given as; } Y_1 = 4 \sin 500\pi t \text{ and } Y_2 = 2 \sin 506\pi t$ $\text{The general progressive wave equation is given by } Y = A \sin 2\pi \nu t$ $\text{By comparing with the general progressive wave equation we get,}$ $\Rightarrow \nu_1 = 250 \text{ Hz, } \nu_2 = 253 \text{ Hz}$ $\text{The beat frequency is given by; } |253 - 250| = 3 \text{ Hz/s}$ $\text{The beat frequency per minute is } 3 \times 60 = 180$ $\text{Hence, option (3) is the correct answer.}$

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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
}