Question

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Suppose g(t)=x(t) cos (t) and the Fourier transform of the g(t) is
G(jw)={1, |w|≤2
{0, otherwise
Determine x(t)

Answer 1

The resulting wave function from the superposition of two waves is y(x, t) = 2A sin(kx)cos(wt).

Step-by-step explanation:

The wave function for the first wave is y₁(x, t) = A sin(kx - wt) and the wave function for the second wave is y₂(x, t) = A sin(kx + wt). To find the resulting wave function from the superposition of these two waves, we add the two wave functions together:

y(x, t) = y₁(x, t) + y₂(x, t) = A sin(kx - wt) + A sin(kx + wt)

Using the trigonometric identity sin(α) + sin(β) = 2sin((α+β)/2)cos((α-β)/2), we can simplify the expression:

y(x, t) = 2A sin(kx)cos(wt)

Therefore, the resulting wave function is y(x, t) = 2A sin(kx)cos(wt).