On Different Wavelengths is a side quest in Fallout: New Vegas.

Quick walkthrough

Side quest: On Different Wavelengths
Find the location of Mojave Music Radio.
Decide which radio station to side with.
Either resolve Mr New Vegas and Mr White's issues, kill one of them, or kill both.
Reward: 500 XP, A new perk, depending on your choice, Variable caps

Detailed walkthrough

Upon meeting Mr New Vegas, he will speak to you in a calm and charismatic manner. After exhausting all of his lines of dialogue, he will gain an extra line, asking him about Mojave Music Radio, and his opinion on it. He says he isn't very fond of the radio station, and asks if you could do him a favor. He asks if you could find Mojave Music Radio, where the station is coming from, and deal with it. Promptly, he will reward you with caps and some knowledge he has. He then gives you a sound-wave tracker and tells you to find it and deal with it, once and for all, sounding quite serious, more cold than usual, too.

Upon using the tracker, you discover that Mojave Music Radio is being broadcasted from Searchlight Airport. You then head there to figure out who is broadcasting it. Upon entry, you are greeted by feral ghouls, who you must defeat to get to the top of the building where it is being broadcasted. You suddenly see a ghoul in a fancy suit, named Mr. White. He shows interest that someone has finally got to him.

When you waste all his conversation lines, you gain yet another one, telling you that he used to be a radio host in pre-War Vegas, and Mr. New Vegas got immortality instead of him, but Mr. White wants to put Mr. New Vegas in his place, and makes a counter-offer.

He gives you a radio jammer, and tells you to jam Radio New Vegas rather than his station. This radio station will then be temporarily malfunctioning until the quest is finished.

Upon choosing which station to jam, either Radio New Vegas or Mojave Music Radio, Mr. White will then head to Radio New Vegas, prepared to deal with Wayne, once and for all. They will begin having a very serious chat, with Wayne aware of who Mr. White once was.

From here, you have four options.
1: You can kill Mr. New Vegas, and gain the perk Old Dogs from Mr. White, which allows you to use melee with ranged weapons, smacking people with the weapon, using less points in VATS.
2: You can kill Mr. White and gain the perk V.I.P from Mr. New Vegas, in which people with substantially lower levels will no longer try to attack you, and can be subdued to be temporary companions.
3: You can kill both and gain the perk Immortality?, which allows you to use an attack every day that uses all of your Action Points, but kills the target in one hit.
4. You can, with 100 Speech, convince both of them to stand down, and gain the perk The Power of Friendship, which gives you +10% extra accuracy and +10% extra damage in VATS when you have companions with you.

After you beat this quest, either Mr. New Vegas will give you 5,000 caps and 500 EXP, or Mr. White will give you that, and you will gain your perk. The surviving radio station(s) will also gain the previously unused song which will be played after the quest: Dear Hearts and Gentle People.