A sinusoidal carrier wave has an amplitude of 5 volts, a frequency of 1MHz, and zero phase angle. Select the correct carrier wave equation.

a. c (t) = 1E6 cos (2π*5*t)

b. c (t) = 5 cos (2π*1E6*t)

c. c (t) = 5 cos (π*2E6*t)

d. either b or c

The correct answer is b.

Step-by-step explanation:

The wave equation is given generally as:

c (x, t) = Acos (kx - wt)

Where A = amplitude

k = wave number

w = angular frequency.

x = horizontal distance moves by the wave.

t = time

The options show to us that the wave depends only on t and not (x, t).

Hence, the wave equation becomes:

c (t) = Acos (wt)

Given that:

A = 5 V

f = 1 * 10⁶ Hz

Angular Frequency, w, is given as:

w = 2πf

w = 2 * π * 1 * 10⁶ Hz

w = 2π (1 * 10⁶)

The wave equation becomes:

c (t) = 5cos (2*π*1*10⁶)

The correct answer is b.