Phase and Amplitude

The Equation (i) for a traveling wave can be generalized by noting that the wave can have an arbitrary amplitude A,

.......(i)

and an arbitrary constant phase angle ∅ to give
y = A sin (kx – ωt + ∅) .....(1)
The amplitude A just makes the sine wave bigger or smaller, and the phase angle ∅ shifts the sine wave to the left or right.
To see precisely how the phase angle ∅ shifts the sine wave, we have in Figure (1) compared sin θ and sin (θ + ∅) . The function sin (θ + ∅) crosses zero when the angle (θ + ∅) = 0 or at (θ = –  ∅) . Thus adding a phase angle ∅ shifts the sine wave back a distance – ∅ radians. If, for example, we set ∅ = π/2 , the wave is shifted back 1/4 of a wavelength, and we have converted a sine wave into a cosine wave.

Figure 1: Adding a phase angleφ shifts the wave back a distanceφ .