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
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.
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