Refer to the diagram shown below.
The suspended wire is in the shape of a parabola defined by the equation
y = ax²
where a = a positive constant.
The derivative of y with respect to x is y' = 2ax.
The vertex is at (0,0) and the line of symmetry is x = 0.
The suspended length is 41 ft, therefore half the suspended length is 20.5 ft.
The length between x = 0 and x = 20 is given by
Because we do not know the value of a, we shall find it numerically.
Define the function
The plot for f(a) versus a yields an approximate solution (from Matlab) of a = 0.01 (shown in the figure).
Therefore
y = 0.01x²
When x = 20 ft, h = 0.01(400) = 4 ft
Because the vertex of the parabola is 19 ft above ground, the support points for the wire are 19 + h = 23 ft above ground.
Answer: 23.00 ft
The siren has a lower pitch as it moves away because crests of the sound are farther apart. Details about sound waves can be found below.
<h3>What is a sound wave?</h3>
Sound wave is thee longitudinal wave of pressure that is transmitted through any plastic material.
A sound wave like every other type of wave posseses wave like features such as wavelength, period etc.
According to this question, as a siren moves away, the pitch gets lower. This can be attributed to the distant crest of the sound wave.
Learn more about sound waves at: brainly.com/question/11797560
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