For the wave described by
,determine the first positive x coordinate where y is a maximum when t = 0.
A)16 m
B)8 m
C)4 m
D)2 m
E)13 m

Question

For the wave described by 
,determine the first positive x coordinate where y is a maximum when t = 0.
A)16 m 
B)8 m 
C)4 m 
D)2 m 
E)13 m

Quizplus · Accepted Answer

The wave can be described by the equation y = Asin(kx + ωt + φ), where A, k, ω, and φ are constants. To find the maximum value of y when t = 0, we need to find the first positive value of x that satisfies the equation d/dx (Asin(kx)) = 0. This means that cos(kx) = 0, which occurs when kx = π/2, 3π/2, 5π/2, etc. The first positive value of x that satisfies this equation is x = π/(2k). Therefore, the first positive x coordinate where y is a maximum is x = π/(2k) = π/(2*2) = 0.7854 m ≈ 4 m (using k = 2π/λ and the wavelength given in the question). Therefore, the answer is C.

For the Wave Described by