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Current Question (ID: 20014)

Question:

$\text{The equation of a progressive wave is given by;}$ $y = A \sin(160t - 0.5x), \text{ where } x \text{ and } y \text{ are in metres and } t \text{ is in seconds. If the speed of the wave is } 10x \text{ m/s, then } x =$

Options:

1. 32
2. 23
3. 16
4. 50

Solution:

$\text{Hint: } v = \frac{\omega}{k}$ $\text{Step: Find the value of } x.$ $\text{The general equation of the progressive wave is given as;} y = A \sin(\omega t - kx)$ $\text{The equation of progressive wave is given by;} y = A \sin(160t - 0.5x)$ $\text{By comparing both equations we get;} \omega = 160 \text{ and } k = 0.5$ $\text{The speed of the wave is given by;} v = \frac{\omega}{k} = \frac{160}{0.5} = 320 \text{ m/s}$ $\Rightarrow 10x = 320 \Rightarrow x = 32$ $\text{Therefore, the value of } x \text{ is } 32.$ $\text{Hence, option (1) is the correct answer.}$

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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
}