Import Question JSON

Current Question (ID: 16013)

Question:

$\text{Stationary waves can be obtained in an air column even if interfering waves have different:}$ $1. \text{ Amplitude}$ $2. \text{ Wavelength}$ $3. \text{ Velocity}$ $4. \text{ Frequency}$

Options:

1. $\text{Amplitude}$
2. $\text{Wavelength}$
3. $\text{Velocity}$
4. $\text{Frequency}$

Solution:

$\text{Hint: Recall the condition for the formation of a stationary wave.}$ $\text{Step: Write down an individual wave for standing waves.}$ $\text{Consider two stationary waves of two different amplitudes.}$ $y_1 = A_1 \sin(kx + \omega t)$ $y_2 = A_2 \sin(kx - \omega t)$ $\text{The velocity of the standing wave is given by;} \; v = \frac{\omega}{k}$ $\text{Therefore, stationary waves can be obtained in an air column even if interfering waves have different amplitudes.}$ $\text{Hence, option (1) is the correct answer.}$

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
}