You are standing 100 meters from an object emitting a sound of constant intensity (loudness). You walk toward the source of sound until you are 20 meters from it. From your perspective, what has happened to the intensity of the sound?

Question

It has decreased by a factor of five.

It has increased by a factor of five.

It has decreased by a factor of twenty-five.

It has increased by a factor of twenty-five.

Answer 1

The intensity of sound follows an inverse square law, which means that the intensity (I) of the sound is inversely proportional to the square of the distance (d) from the source. Mathematically, this is expressed as:

\[ I \propto \frac{1}{d^2} \]

Initially, you are 100 meters from the sound source. When you walk closer to it, the distance becomes 20 meters. To find the change in intensity, we can compare the intensities at these two distances.

1. At 100 meters: \[ I_1 \propto \frac{1}{100^2} = \frac{1}{10000} \]

2. At 20 meters: \[ I_2 \propto \frac{1}{20^2} = \frac{1}{400} \]

Now we can find the ratio of the two intensities:

\[ \frac{I_2}{I_1} = \frac{\frac{1}{400}}{\frac{1}{10000}} = \frac{10000}{400} = 25 \]

This means that the intensity of the sound has increased by a factor of 25 as you moved from 100 meters to 20 meters away from the source.

So, the correct answer is:

It has increased by a factor of twenty-five.