The Question is from neet-physics waves velocity-of-sound, and it was created by the author Mr. ANIL KUMAR.G

Question

A sound wave travels through a medium with a bulk modulus $B$ and density $\rho$. If the medium is suddenly compressed such that its density becomes $1.5\rho$ while the temperature remains constant, what is the new speed of sound in the medium?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Speed of Sound in a Medium
	**Related Topics**: Bulk Modulus, Density, Wave Propagation
	**Prerequisites**: Relationship between speed of sound, bulk modulus, and density.
## SOLUTION PATHWAY
**Given Information**:
	* Initial density: $ho$
	* Final density: $1.5ho$
	* Bulk modulus: $B$ (remains constant as temperature is constant)
	* Temperature remains constant.
**Method & Steps**:
	1. Recall the formula for the speed of sound in a medium.
		Reasoning: The speed of sound ($v$) in a medium is related to the bulk modulus ($B$) and density ($ho$) of the medium.
		Formula/Rule: $v = \sqrt{\frac{B}{ho}}$
	2. Determine the new speed of sound ($v'$) when the density changes to $1.5ho$.
		Working: $v' = \sqrt{\frac{B}{1.5ho}} = \sqrt{\frac{1}{1.5}} \sqrt{\frac{B}{ho}} = \frac{1}{\sqrt{1.5}}v = \frac{v}{\sqrt{1.5}}$
		Key Point: Since the temperature remains constant, the bulk modulus $B$ remains constant.
	3. Express the new speed of sound in terms of the original speed.
		Result: $v' = \frac{v}{\sqrt{1.5}}$
		Verification: The new speed of sound is inversely proportional to the square root of the density. Since the density increases, the speed of sound decreases.
## OPTION ANALYSIS
[A] :x: This option suggests the speed remains unchanged, which is incorrect as the density has changed.
[B] :x: This option suggests the speed increases, which is incorrect as the density has increased, and speed is inversely proportional to the square root of density.
[C] ✓: This option correctly represents the decrease in speed due to the increased density. The new speed is the original speed divided by the square root of the factor by which the density increased.
[D] :x: This option suggests a direct increase in speed proportional to the increase in density which is incorrect. 
## LEARNING AIDS
	**Common Mistakes**:
		1. Assuming the bulk modulus changes with density: The bulk modulus can be considered constant as long as the temperature remains constant.
		2. Forgetting the square root:  The speed of sound is proportional to the square root of B and inversely proportional to the square root of $ho$.
	**Quick Tips**:
		1. Remember the relationship: $v \propto \sqrt{\frac{B}{ho}}$
		2.  If density increases, speed decreases and vice-versa, assuming constant temperature.

Mr. ANIL KUMAR.G · Answer

v

Mr. ANIL KUMAR.G · Answer

\sqrt{1.5}v

Mr. ANIL KUMAR.G · Answer

The correct Option is "\frac{v}{\sqrt{1.5}}"

Mr. ANIL KUMAR.G · Answer

1.5v

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