Question Detail

PHY 104 Wave and sound Objective Question
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Question

The document states that the velocity of a longitudinal pulse in a medium is given by v = √(B/ρ₀), where B is the bulk modulus and ρ₀ is the undisturbed density. How does the speed of sound relate to the rigidity and density of the medium based on this formula?
Options
A Speed increases with decreasing rigidity and increasing density.
B Speed increases with increasing rigidity and increasing density.
C Speed increases with increasing rigidity and decreasing density.
Correct Answer
D Speed decreases with increasing rigidity and decreasing density.
Correct Answer

Option C is the correct answer.

Detailed Explanation

From the formula v = √(B/ρ₀), the speed v is directly proportional to the square root of the bulk modulus B, which is a measure of a material's resistance to compression (rigidity). Thus, increasing rigidity (B) increases speed. The speed v is inversely proportional to the square root of the density ρ₀. Thus, decreasing density (ρ₀) increases speed. This is also explicitly stated on page 14: 'Thus, the more rigid a solid, the higher the bulk modulus and the faster the velocity of sound in it.'

Hint

Analyze the formula v = √(B/ρ₀). Rigidity is related to the Bulk modulus (B).

Question Info

Course: PHY 104
Topic: Wave and sound
Type: Objective
Difficulty: Not specified
Question 333 of 947
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