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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?

Respuesta :

okpalawalter8

Answer:

The intensity at distance 2d from source is  [tex]I_1 = \frac{1}{4} * I[/tex]  

Explanation:

From the question we are told that

     The distance of the wave from point source is  d  

     The  intensity is  [tex]I[/tex]  

     The distance we are considering is  2d

Generally the intensity of a wave is mathematically represented as

            [tex]I = \frac{ P }{\pi d^2 }[/tex]    

Here P is power of point source      

Now when  d =  2d

          [tex]I_1 = \frac{ P }{\pi (2d)^2 }[/tex]        

           [tex]I_1 = \frac{ 1 }{4 } * \frac{ P }{\pi d^2 }[/tex]

    =>   [tex]I_1 = \frac{1}{4} * I[/tex]  

Lanuel

The intensity at a distance 2d from the source is equal to [tex]I'=\frac{I}{4}[/tex]

Given the following data:

  • Distance = d
  • Intensity = I

To determine the intensity at a distance 2d from the source:

Mathematically, the intensity of a wave is given by the formula:

[tex]I=\frac{P}{\pi d^2}[/tex]

Where:

  • I is the intensity of a wave.
  • P is the power.
  • d is the distance.

Since the distance is doubled (2d), we have:

  • Let the new intensity be [tex]I'[/tex]

[tex]I'=\frac{P}{\pi (2d)^2}\\\\I'=\frac{P}{4\pi (d)^2}\\\\I'=\frac{1}{4} \times \frac{P}{\pi (d)^2}\\\\I'=\frac{1}{4} \times I\\\\I'=\frac{I}{4}[/tex]

Find more information: https://brainly.com/question/23460034