Question

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

Answer 1

Answer:

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.