Question

The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source?

Answer 1

The intensity of waves from a point source is inversely proportional to the square of the distance from the source. When the distance is doubled, the intensity becomes one-quarter of the original. This is known as the Inverse Square Law.

Step-by-step explanation:

If the intensity of waves from a point source at a distance d from the source is I, then the intensity at a distance 2d from the source, according to the Inverse Square Law, would be I/4. This law states that the intensity (I) of a wave is inversely proportional to the square of the distance (d) from the source, assuming the wave radiates uniformly in all directions and there are no absorption or interference effects.

For example, if the intensity of a 120-W lightbulb observed from 2 m away is 2.4 W/m², when the distance is doubled to 4 m, the new intensity would be 2.4 W/m² ÷ 4, which equals 0.6 W/m². The decrease in intensity as distance increases is a fundamental behavior of electromagnetic waves and sound waves, both of which follow an inverse square relationship with distance.

Answer 2

The intensity at distance 2d from source is
`I_1 = (1)/(4) * I`

Step-by-step explanation:

From the question we are told that

The distance of the wave from point source is d

The intensity is
`I`

The distance we are considering is 2d

Generally the intensity of a wave is mathematically represented as

`I = ( P )/(\pi d^2 )`

Here P is power of point source

Now when d = 2d

`I_1 = ( P )/(\pi (2d)^2 )`

`I_1 = ( 1 )/(4 ) * ( P )/(\pi d^2 )`

=>
`I_1 = (1)/(4) * I`