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Waves question

2025 · 28 Jan · Shift 1 · Q52
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Waves question

2025 · 28 Jan · Shift 1 · Q52

JEE MainPhysicsWavesMCQ+4 / −1
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R\mathbf{R}R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below
  1. A
    Both A\mathbf{A}A and R\mathbf{R}R are true and R\mathbf{R}R is the correct explanation of A\mathbf{A}A
  2. B
    A\mathbf{A}A is false but R\mathbf{R}R is true
  3. C
    A\mathbf{A}A is true but R\mathbf{R}R is false
  4. D
    Both A\mathbf{A}A and R\mathbf{R}R are true but R\mathbf{R}R is NOT the correct explanation of A\mathbf{A}A
View written solutionFree

Correct answer: C

  1. Use the formula for speed of sound

    The speed of sound in a medium is generally given by v=elastic modulusρv = \sqrt{\frac{\text{elastic modulus}}{\rho}}v=ρelastic modulus​​ where ρ\rhoρ is the density of the medium.

    • In gases, the relevant elastic modulus is the bulk modulus BBB.
    • In solids, sound speed is larger because solids have much greater elastic stiffness.

  2. Check Assertion A

    Assertion A: A sound wave has higher speed in solids than gases.

    This is true.

    Typical values:

    • In air: about 340 m/s340\,\text{m/s}340m/s
    • In solids like steel: several thousand m/s\text{m/s}m/s

    So sound indeed travels faster in solids than in gases.

  3. Check Reason R

    Reason R: Gases have higher value of Bulk modulus than solids.

    This is false.

    In fact, solids generally have much higher elastic modulus/bulk modulus than gases. Gases are highly compressible, so their bulk modulus is much smaller.

  4. Conclusion

    • Assertion A is true.
    • Reason R is false.

    Therefore, the correct option is: C\boxed{\text{C}}C​

  5. Comparison with stored answer

    Stored correct answer: C

    This matches the derived answer.

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