Question

Which of the following functions illustrates a change in amplitude?

a. y = tan 2x
b. y = -2 - cos(x-π)
c. y = 1 sin x
d. y = 3 cos 4x

Answer 1

The function 'y = 3 cos 4x' illustrates a change in amplitude, with the number '3' indicating the amplitude of the wave. Amplitude is shown by the coefficient preceding the sine or cosine term in a trigonometric function.

Step-by-step explanation:

The function that illustrates a change in amplitude from the options given is y = 3 cos 4x. Amplitude is a measure of how far the peaks and troughs of a wave are from the equilibrium position. It can be identified in a trigonometric function as the coefficient before the sine or cosine function. In this case, the coefficient '3' indicates that the amplitude of the cosine wave is 3. The amplitude of a wave is typically represented by the letter 'A' in the wave function, such as y(x, t) = A sin(kx - ωt + φ) or y(x, t) = A cos(kx - ωt + φ).

Two waves with the same amplitude and a phase difference of 180° (or π radians) would cancel each other out, resulting in a resultant amplitude of 0, as the waves would be exactly out of phase and thus undergo destructive interference.