This is the sort of function you might actually measure in a lab. It is purely real, so its spectrum is Hermitian: the real part is even and the imaginary part is odd. For a sine wave the real part is zero.

Try It Yourself

ℱ→

𝜈=0 𝜈=32
Slider for setting frequency

ϕ=0 ϕ=π/2
Slider for setting phase

Remarks

For a sine wave, the spectrum is purely imaginary; for a cosine wave it is purely real. For a wave whose phase is between that of sine and cosine, you get both real and imaginary parts, with Hermitian symmetry.

The next page in this sequence will show you how to add sine waves to build up other kinds of waves.