wave, waive, waver, waiver

Wave or wave means to move the hand back and forth or to move something back and forth--
They taught the baby to wave good-bye.
Crowds at stadiums now do the wave.
Wave may also mean the movement of the ocean--
The surfer waited to catch a wave.
The next wave may knock down our sand castle.
Wave may mean something with a ripple in it, like hair--
Grandmother used to go to the beauty parlor for a permanent wave.
There are waves we can't see, like radio waves--
Light is considered to be both a wave and a particle.

Waive or waive ( rhymes with wave ) means to make an exemption  from a rule or requirement--
If you ask, they may waive the entrance fee.
The personnel department may waive the education requirement, and accept experience instead.

Waver or waver means to vacillate, or go back and forth in one's opinions or ideas, to be unable to make up one's mind, or make a decision--
The reporter always noticed a politician who seemed to waver.
If they notice that you waver, they will not believe you.

Waiver or waiver ( rhymes with waver ) means an exemption from the usual rules or procedures--the thing granted in this way, either the piece of paper itself, or the idea--
They granted him a fee waiver.
I hope they accept my request for a waiver.

Now that you know that, you can say--
"The fans asked them to waive the rule against doing the wave."
"The dean seemed to waver when I asked for a waiver."

Note--a "wafer" is a sort of cracker or cookie or a small piece of flat bread--
She was superstitious about choking on a communion wafer.
Note #2--a person waving might be called a "waver"--
A waver fell down at the football game.
Something used to wave hair might also be called a "waver"--
She used the waver to do her hair. It looks nice.
Note # 3--a person wavering might be called a waverer--
He is such a waverer. He can never make up his mind.
Note # 4--not to be confused with "wavier" ( wave ee err ) , meaning more wavy than--
His hair is wavier than hers.
Note # 5--a "wayfarer" ( way fare err ) is someone who is on a journey--
The wayfarer asked if he might sleep in the barn.
Note # 6--a "waif" is a poor or homeless child--
They took the poor little waif home and found her some warm clothing.