2006-08-13 02:55:45 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Engineering
Yes.
Any periodic wave has a sinusoidal property.
Any waveform can b approximated by Fourier series.
2006-08-13 03:15:59 · answer #1 · answered by Edward 7 · 0⤊ 0⤋
If you are asking if the profile of water waves is the same as a single sinusoidal waveform, the answer is NO. The wave is not that uniform. If you are asking if the water wave can be expressed as multiple sinusoidal waveforms, then the answer is YES. The shape of water waves can be expressed through a Fourier series as multiple sinusoidal waveforms combined into a single waveform.
2006-08-13 23:04:37 · answer #2 · answered by anim8er2 3 · 0⤊ 0⤋
Yes. Any periodic function can be described by a series of sine and/or cosine functions added together. This is known as Fourier Series.
For example imagine a wave that is 0 for interval 0 to pi and then 1 for pi to 2pi and that repeats itself (known as a square wave to EEs).
That square wave can be approximated by this summation:
1/1sin x + 1/3 sin 3x + 1/5 sin 5x + 1/7 sin 7x + ..... 1/n sin(2n-1)x for n = 1 to infinity!
If you make a wave that is y = x for interval 0 to pi and then y = -x from pi to 2pi then that wave can be described as:
1/1 cosx + 1/9 cos3x + 1/25 cos 5x + 1/49 cos 7x +....1/n^2 cos (2n-1)x
An astute reader my notice that the bottom wave is the integral of the square wave!
If you shoot an electrical square wave into an "integrating circuit" you will see a triangular wave form on the output (as measured with an oscilloscope)!
Therefore, any type of periodic waveform can be approximated by a Fourier Series.
Here is an easy one for you:
F(t) = sin (2pi*t/365.25) care to guess what that one is??
2006-08-13 12:08:27 · answer #3 · answered by cat_lover 4 · 0⤊ 0⤋
You bet!
2006-08-13 11:34:45 · answer #4 · answered by Kes 7 · 0⤊ 0⤋