Import Question JSON

Current Question (ID: 15972)

Question:

$\text{A bat emits an ultrasonic sound of frequency } 1000 \text{ kHz in the air. If the sound meets a water surface, what is the wavelength of the reflected sound? (The speed of sound in air is } 340 \text{ m/sec and in water is } 1486 \text{ m/sec)}$

Options:

1. $3.4 \times 10^{-4} \text{ m}$
2. $1.49 \times 10^{-3} \text{ m}$
3. $2.34 \times 10^{-2} \text{ m}$
4. $1.73 \times 10^{-3} \text{ m}$

Solution:

$\text{Hint: The frequency of sound does not depend on the medium.}$ $\text{Step: Calculate the wavelength of reflected sound.}$ $\text{The frequency of sound in air and in water is the same.}$ $\lambda_{\text{air}} = \frac{v_{\text{air}}}{f}$ $\lambda_{\text{air}} = \frac{340}{1000 \times 10^3}$ $\lambda_{\text{air}} = 3.4 \times 10^{-4} \text{ m}$ $\text{Therefore, the wavelength of reflected sound is } 3.4 \times 10^{-4} \text{ m.}$ $\text{Hence, option (1) is the correct answer.}$

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
}