Hello from Finland. I am a Senior Electronic Maintenance Engineer having serviced TV-studios for 25 yrs. I'm also a Radio Technician and have been working in Finnish Telecommunication Radio Laboratory. Moreover I am Radio Amateur so I have quite much experience about radio transmitters.

It looks that Thumpers can make interferences with TV-studio equipments like wireless mics. What kind of problems have you had? There are not many free frequencies which you can use without license worldwide. Many countries have strict regulations as we have here in Finland.

Also I've seen thumpers with a whip antenna which looks odd to me as it is not very handy, is not very sturdy and shows that these are probably made cheaply as the real professional transmitters are more "sealed". Also there should be a good coding to prevent accidental triggerings. In matter of fact, If you don't tell anybody, I can reveal that I've been using a cheap wireless doorbell, which is very reliable due to well integrated structure. =)

Okey. No single reply. Actually I'm not surprised because cheap toy transmitters (fart pillows etc.)
use very simple radio technique and do not have any bad frequencies or modulation which could affect
audio or video equipments. Cell Phone is much worse because the signalling is really challenging which
you can easily hear if you put the phone near audio amplifier, TV or radio. If you are worrying about
possible interference to let's say wireless mics, you can test the radio transmitter with portable
radio. Choose different wavebands like FM and LW and if nothing can be heard, you are 99.99 % safe.
Now you must understand that if your radio is on the same frequency band, the transmitter probably
gives some kind of sounding, clicking etc. which is not disturbance but normal behavior.

The reason I wrote this, is that some radio transmitters can cost really much and they are usually
sold as safe on TV-studios or so. One you should keep in mind is the receiver, if it has relays.
If the relay cuts large currents, it may cause clicks. Those are quite easy to kill and you can test
this using LW (or MW, SW) waves. In a good situation you may hear something if you are near the radio.
If you increase the distance between them, let's say few feet, it should be enough.

Hope you got the idea. I'm not saying that you shouldn't buy expensive equipments if you can afford them.