Question Detail
Question
The document states that the intensity of a sound wave falls with distance in an inverse-square manner, meaning I ∝ 1/r². If the intensity of sound at point A (distance r_A from the source) is I_A, and at point B (distance r_B from the source) is I_B, what is the ratio I_A / I_B?
Correct Answer
Option B is the correct answer.
Detailed Explanation
From the relationship I ∝ 1/r², we can write I = k/r² for some constant k. Therefore, I_A = k/r_A² and I_B = k/r_B². The ratio I_A / I_B = (k/r_A²) / (k/r_B²) = r_B² / r_A². This is directly illustrated in the 'Problem' example on page 20, where I_A : I_B : I_C = 1/r_A² : 1/r_B² : 1/r_C².
Hint
Use the inverse-square relationship I = k/r² and set up the ratio of intensities. Ensure the distances are correctly inverted and squared.