Conversion of .wav to mp3 file?

I am co-host of a radio program broadcast by satellite by NPR. They recently switched from allowing downloads of our programs from mp2 files to .wav. I formerly used iTunes to convert the mp2s to mp3s for uploading on our website for listeners who preferred to listen to the show in mp3 form. No matter what I do, using iTunes, Switch, I cannot get any of them to recognize and convert the .wav file to mp3. I have the "Read and Write" permissions clicked but iTunes doesn't even give me a failure message. The other two shareware programs have given me an error message that recommends checking permissions. I am stymied and would appreciate any suggestions. And I have contacte NPR Satellite systems for their suggestions as well.
Thanks ahead of time for anything that will unlock this mystery.

Have you tried importing the files into iTunes as AAC's to see if you can actually convert the .wav's at all...

Conversion of .wav

Not used to manipulating iTunes, I tried setting the preferences for all the optional formats under "Preferences/Import." None of them seem to touch the .wav file at all so far. It's almost as if there's something blocking my Mac from reading the .wav file or as if the .wav file is corrupted somehow but I have downloaded it three times with the same results. (I'm also asking NPR for help but nothing so far.) Thanks for your suggestion.

You'll need another app like SoundGrinder to do the conversion.

I've used this program to convert a bunch of stuff I had in .wav format and it works well.

What's the name of your show on NPR?

mp3 conversion

The name of the show is "THE BOOK GUYS" and it turns out that the PRSS (Public Radio Satellite Service) .wav files are not normal .wav files, therefore iTunes and other programs didn't recognize it. I finally found one called "Audacity" (freeware) that works fine and we are now all set. Thanks for the suggestions!!