They ask you to model the radio waves as being driven by a sinusoidal source (co

Question

They ask you to model the radio waves as being driven by a sinusoidal source (could mean a sine or cosine wave, which one it is, depends on the following statements) with a frequency of 3000 Hz with the magnitude of the vertical displacement between the crest of one wave and the trough/valley of another is 2.00 m. The vertical displacement is symmetric about the origin in the y-dimension. Since these waves are radio waves they travel at nearly the speed of light (3.0 × 108 m/s). At t = 0 s, a wave crest, at its maximum vertical displacement, passes your testing equipment at your research location (this is the origin, x-0 m, for the system). (A) What is the magnitude of the amplitude A, angular Frequency w, period T, wavelength A, and wave number k describing the waves in your surrounding research location under these conditions (basically what is the wave equation y Acos(kx-wt) at your location, fill in for A, k, and w and write this equation down using the numerical values you found)? (B) Given the above conditions, which remain constant, what is the mathematical equation that describes the vertical position of the wave as a function of time only for neighboring testing equipment located a positive 48,270 m (30 miles) away from your original testing location (Note: the waves move toward your equipment in the positive direction from the original testing location at x 0 m)?

Explanation / Answer

A) Amplitude, A = 2.00 m

angular frequency, w = 2*pi*f

= 2*pi*3000

= 18849.56 rad/s

T = 1/f

= 1/3000

= 3.33*10^-3 s

lamda = v/f

= 3*10^8/3000

= 10^5 m

k = 2*pi/lamda

= 2*pi/10^5

= 6.28*10^-5 m

y = 2*cos(6.28*10^-5*x - 18849.56*t) <<<------Answer

B) at x = 48270 m

y = 2*cos(6.28*10^-5*48270 - 18849.56*t)

= 2*cos(3.03 - 18849.56*t) <<<------Answer

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