Question

This kind of decomposition of a wave pattern into frequencies is bread and butter for electrical engineers! This is why they are all very keen on complex numbers and their magic. Here is a similar question as the last, but this time you want to create the wave y=sin x using a linear combination of the constituent functions 1, cos 22 and cos 4x to form 4 a+b cos 2x + c cos 4x. How much of each do you need? a = 0 b = 0 C = 0 2 1 -2 -1 0 2 3 My best values were a = Number b= Number C Number

Answer 1

The student's question involves creating a wave y = sin x using a linear combination of 1, cos 2x, and cos 4x, which cannot be achieved due to phase and frequency differences.

Step-by-step explanation:

The question relates to the decomposition of a wave pattern into its constituent frequencies using a linear combination, which is a fundamental concept in physics, particularly in the study of waves and their properties such as amplitude and frequency.

When you need to create a wave y = sin x using a linear combination of constituent functions 1, cos 2x, and cos 4x, you are looking for coefficients a, b, and c such that y can be represented as a + b cos 2x + c cos 4x.

However, sin x cannot be represented as a combination of these functions because it is out of phase with cos 2x and cos 4x and also includes a frequency component that cannot be created by summing cosine functions at different frequencies without introducing a phase shift.