Final answer:
The equation representing the wave with a given amplitude, frequency, and speed of light is y(x,t) = 0.35 m · sin((2.20×10^-2 rad/m)x - (6.58×10^6 rad/s)t), where the wavelength is 285.71 m.
Step-by-step explanation:
To determine the equation that correctly represents a wave with an amplitude of 0.35 m, a frequency of 1.05×106 Hz, and a speed of light (3.00×108 m/s), we first need the wavelength λ. Using the relationship c = fλ, we can find the wavelength by rearranging the equation to λ = c/f.
The wavelength (λ) can be calculated as:
λ = · (3.00×108 m/s) / (1.05×106 Hz) = 285.71 m
The wave equation is generally given as y(x,t) = A sin(kx - ωt), where A is the amplitude, k is the wave number, and ω is the angular frequency. Since k = 2π/λ and ω = 2πf, we can substitute the known values to find these parameters.
k = (2π) / (285.71 m) ≈ 2.20×10-2 rad/m
ω = (2π) · (1.05×106 Hz) = 6.58×106 rad/s
Finally, the wave equation for this electromagnetic wave traveling in the positive x direction is:
y(x,t) = 0.35 m · sin((2.20×10-2 rad/m)x - (6.58×106 rad/s)t)