What would cause a strange whooshing sound when I apply brakes?

This answer seems reasonable. The sound is like a bicycle tire pump that is not hooked to a tire. I did let the brake fluid level get very low and refilled the master cylinder. The sound is inside the cab and has always been there, but not as loud as it is now, and more fluid did not help. Sounds like the booster may be the problem. Is is located just inside the engine compartment on the firewall? How difficult is it to change?

The booster is not 'the problem' , it is more likely a RESULT of the master cylinder failing and the fluid leaking into the booster , as I said before. Pushrod also elaborates to that possibility. Unbolt M/C from booster and separate (No need to disconnect lines yet , unless they prevent the M/C from moving back far enough) far enough to see if it is in fact wet with fluid between the two. IF it is , then you need to replace both , most likely. In some cases , I believe they sell master cyl. and booster combinations 'loaded'. Be sure to properly 'bench bleed' the new M/C , extremely important , to avoid a lot of frustration trying to bleed the rest of the system. Hope some of this helps. Good luck.

Thanks. I'll try that.