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An audio speaker producing a steady sound at an outdoor concert is 20 ft away from you. If you move to a position where the speaker is 62 ft distant, by what factor will the amplitude of the sound change

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okpalawalter8

Answer:

The factor by which the amplitude would change is  k = 0.336

Explanation:

From the question we are told that

   The distance away from the observer is  [tex]d = 20\ ft[/tex]

    The new position of the observer is  [tex]d_1 = 62 \ ft[/tex]

Generally amplitude is inversely proportional to distance

   

Let A denote the amplitude of the sound at d

So  

     [tex]A = \frac{1}{d}[/tex]

Now the amplitude at a distance 62 ft from the speaker can be mathematically represented as

       [tex]A_1 = \frac{d}{d_1} * A[/tex]

 substituting values

       [tex]A_1 = \frac{20}{62} * A[/tex]

       [tex]A_1 = 0.336 A[/tex]

so the factor by which the amplitude would change is  k = 0.336

 

raphealnwobi

The amplitude of the sound change by a factor of 0.336.

Amplitude of sound is inversely proportional to distance.

A ∝ 1/d

A = 1/d

where A is the amplitude and d is the distance

For a distance (d) of 20 ft let the amplitude be A.

If the distance is moved to 62 ft. (d₁), let the new amplitude be A₁. Hence:

[tex]A_1=\frac{d}{d_1}*A\\\\A_1=\frac{20}{62}*A\\\\A_1=0.336A\\[/tex]

Therefore, The amplitude of the sound change by a factor of 0.336.

Find out more at: https://brainly.com/question/2845956

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