Question

Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\):
Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.

• A. \(A\) is false but \(R\) is true
• B. Both \(A\) and \(R\) are true and \(R\) is the correct explanation of \(A\)
• C. Both \(A\) and \(R\) are true but \(R\) is NOT the correct explanation of \(A\)
• D. \(A\) is true but \(R\) is false

Hint:

Always verify the physical properties involved in physics problems to understand the underlying principles correctly.

Answer 1

The Correct Option is D

Step 1: Evaluate the truth of \(A\) and \(R\). Sound travels faster in solids than in gases due to the higher density and elastic properties of solids, not gases.

Step 2: Determine the correctness of \(R\). In fact, solids generally have a higher Bulk modulus than gases, contradicting the statement of \(R\).

Conclusion: Assertion \(A\) is true, stating that sound waves travel faster in solids is correct, but Reason \(R\) is false as gases typically have a lower Bulk modulus than solids.

Answer 2

Step 1: Understand the given statements.
Assertion (A): A sound wave has higher speed in solids than in gases.
Reason (R): Gases have higher value of Bulk modulus than solids.

Step 2: Recall the formula for the speed of sound.
The speed of sound in a medium is given by:
\[ v = \sqrt{\frac{B}{\rho}} \] where:
\( B \) = Bulk modulus of the medium (measure of its elasticity), and \( \rho \) = density of the medium.

Step 3: Analyze the assertion (A).
In solids, the value of the bulk modulus \( B \) is very high, meaning solids are much more rigid and resist compression more strongly than gases. Therefore, the speed of sound in solids is higher than in gases.
Hence, Assertion (A) is true.

Step 4: Analyze the reason (R).
The reason states that gases have higher bulk modulus than solids, which is incorrect. In reality, solids have a much higher bulk modulus than gases because they are less compressible.
Hence, Reason (R) is false.

Step 5: Conclusion.
The correct conclusion is that the assertion is true, but the reason is false.

Final Answer:
\( A \) is true but \( R \) is false.