Suppose the electric field associated with the radio transmissions of a medical

Question

Suppose the electric field associated with the radio transmissions of a medical helicopter is given by E(x, t) = (700 mu N/C) cos[(70 times 10^-2 pi m^-1)x - (210 pi times 10^6 s-^1)t] Determine the wave number of the electromagnetic wave associated with the electric field. (Express your answer to three significant figures.) middot pi times 10^-2 rad/m Determine the angular frequency of the electromagnetic wave associated with the electric field. (Express your answer to three significant figures.) middot pi times 10^6 rad/s Determine the wavelength of the electromagnetic wave associated with the electric field. (Express your answer to three significant figures.) Determine the frequency of the electromagnetic wave associated with the electric field. (Express your answer to three significant figures.) MHz

Explanation / Answer

Given electric field, E = 700 micro N/ C cos(70*10^-2 *pi x - 210*pi*10^6 t)

1. a wave equation is given by E = Eo cos(kx - wt)
here k is angular wave number
so by comparing, k = 70*10^-2 pi rad/m

2) from the same equation, after comparing
w = 210 *pi *10^6 rad/s

3) let the wavelength be lambda
then k = 2*pi/lambda
lambda = 2*pi/k = 2*pi/70*10^-2*pi = 100/35 = 2.857 m

4) similiarly, w = 2*pif
so, f = w/2*pi = 210*10^6 *pi / 2pi = 105*10^6 Hz = 105 MHz

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