Creating a smooth wave background in Adobe Illustrator is quick and easy with these simple steps:
Step 1: Draw Wave Lines
Select the Pencil tool and draw two wave lines.
Set a solid color stroke for the first wave, and apply a gradient stroke to the second.
Step 2: Blend the Waves
Select both wave lines.
Go to Object > Blend > Make to blend the two lines together.
Step 3: Adjust the Blend
To refine the blend, navigate to Object > Blend > Blend Options.
Choose Specified Steps and set the number to around 25 for a smooth transition.
Step 4: Create a Clipping Mask
Draw a new rectangle that covers the entire area of your waves.
Select both the rectangle and the blended waves, then go to Object > Clipping Mask > Make to finalize your wave background.
Just a note: there is no need to use a gradient, I mentioned it for illustration purposes only. In this case, I also added opacity to the first object for a smoother appearance.