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

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

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