Answer:
The sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42
Step-by-step explanation:
The given wind parameters in the wind tunnel are;
The slowest speed of the wind in the wind tunnel, v₁ = 13 feet per second
The maximum speed of the wind, v₂ = 71 feet per second
The time it takes the wind to complete one cycle = 44 seconds
Therefore, we have;
The general form of the sine equation is given as follows;
The period, T = 44 seconds = 2·π/B
∴ B = 2·π/44 = π/22
Given that the wave starts at the slowest speed, the horizontal shift
The amplitude, A = (v₂ - v₁)/2
∴ A = (71 ft./s - 13 ft./s)/2 = 29 ft./s
The vertical shift, D = v₁ + a = 13 ft./s + 29 ft./s = 42 ft./s
D = 42 ft./s
When x = 0, sin(B·C) = -1
∴ -B × C = -π/2
∴ C = π/2 ÷ B = π/2 ÷ (π/22) = π/2 × 22/π = 11
Therefore, the sine equation for the wave is;
the sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42