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Assertion : The speed of soun in solids ...

Assertion : The speed of soun in solids is maximum though density is large.
Reason : The coefficient of elasticity of solid is large.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that the speed of sound in solids is maximum even though the density is large. - **Speed of Sound Formula**: The speed of sound \( V \) in a medium is given by the formula: \[ V = \sqrt{\frac{E}{\rho}} \] where \( E \) is the modulus of elasticity and \( \rho \) is the density of the medium. 2. **Analyzing Density**: - In general, solids have a higher density compared to liquids and gases. However, the speed of sound is not solely dependent on density; it also depends on the elasticity of the medium. 3. **Understanding the Reason**: The reason states that the coefficient of elasticity of solids is large. - **Elasticity in Solids**: Solids have a much higher modulus of elasticity (like Young's modulus) compared to liquids and gases. This means that solids can transmit sound waves more efficiently despite their higher density. 4. **Combining Both Statements**: - From the formula \( V = \sqrt{\frac{E}{\rho}} \), we can conclude that even though the density \( \rho \) of solids is large, the high value of elasticity \( E \) in solids leads to a higher speed of sound \( V \). - Therefore, the assertion that the speed of sound in solids is maximum is true. 5. **Conclusion**: - Both the assertion and the reason are true, and the reason explains the assertion. Thus, the correct conclusion is that both statements are true, and the reason provided supports the assertion. ### Final Answer: Both the assertion and reason are true, and the reason explains the assertion.
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that the speed of sound in solids is maximum even though the density is large. - **Speed of Sound Formula**: The speed of sound \( V \) in a medium is given by the formula: \[ ...
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