Question

A source of sound is 30 cm from the first listener A's ear and 1.50 m from the second
listener B's ear. What is the difference between the sound intensity levels heard by the two listeners,
knowing that the sound intensity is inversely proportional to the square of the distance from the source to
the listener?

Answer 1

Answer:

The intensity at A is 25 times greater than the intensity at B.

Explanation:

Intensity is inversely proportional to the square of the distance from the source:

I = k / d²

For the first person:

I₁ = k / (0.30)²

I₁ = k / 0.09

For the second person:

I₂ = k / (1.50)²

I₂ = k / 2.25

Finding the difference would require knowing the constant of proportionality, which isn't given.  We can, however, find the quotient.

I₁ / I₂ = (k / 0.09) / (k / 2.25)

I₁ / I₂ = 2.25 / 0.09

I₁ / I₂ = 25

The intensity at A is 25 times greater than the intensity at B.