If there is no hum when the cable is plugged into the instrument and the amplifier, there is no problem. Without the instrument, the cable is acting as an antenna, sending a 60Hz signal to the amplifier input. This is a common issue with lots of electrical measuring equipment and audio gear.

If you Google "how should you connect a guitar to an amplifier?" you will see that you are supposed to plug the cable into the guitar first, and then plug the cable into the amplifier before turning on the power.

In some cases, a bad cable can cause the same thing, but that probably isn't the issue.

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RF or radio frequency interference is caused by unwanted external signals or electrical energy. It can be from items I mentioned below and also by bad shielding in the cable.

My son, a professional musician who plays guitar, uses these in small venues. He is very pleased with them. A major problem with wireless systems is interference from other devices that may be on the same frequency. Older devices are more prone to this than new ones due to the changes by the FCC in frequency usage and allocation.

Ken

"The dulcimer sings a sweet song."

I have this system and it works great!

Amazon.com: Upgrade 2.4GHZ Wireless Guitar System Built-in Rechargeable Lithium Battery Wireless Guitar Transmitter Receiver for Electric Guitar Bass : Musical Instruments

If I do not have a cable connected to the amplifier at all then the amplifier doesn't hum but if I plug in the cable to the amplifier and the other end is not plugged into the instrument I get that home I don't believe I get the hum if it's plugged into the amplifier and the instrument. Oh Ken what is a RF interference

Also

Does anyone know anything about a device that you can plug into your instrument and then the other end goes to the amplifier? I think it's called some kind of transmitter(s)  . It looks like you plug in the transmitter into the instrument and then a receiver into the amplifier. That way You don't need a cord, however there's something about frequencies not sure what that has to do with anything but apparently you need to take that into consideration when purchasing these units anybody out there have an idea on  a good brand is to buy and can explain this thing about frequencies thanks again 

First question: Did you have it plugged into your dulcimer before plugging the cable into the amp? Second question: Does the hum also happen without the cable plugged in? Generally there are two reasons for a hum; a ground fault or RF interference. If the amp has a three prong plug and is plugged into a grounded outlet there shouldn't be a hum. If there is a hum, it could be the cable, a ground problem with amps wiring, or RF interference. If it is RF interference look for a florescent light nearby or something with a motor (refrigerator, fan, air conditioner, etc.) If that is the case try moving the amplifier away from that source of interference. This can also happen if one of those items is plugged into the same outlet or circuit as the amp.

Ken

"The dulcimer sings a new song."

Oh I forgot it's a relatively modern amplifier it's not a tube type it's digital 

Well I just bought a new toy. And I have a question. I I bought a used amp, I've never had an amp before so the question is.  I have the amp turned on low volume and when I plug in a cord it hums like crazy even though the other end of the court is not connected to an instrument is that normal ? If the court is not plugged into the amp at all there's no hump it's only when I plug in the cord  ( Thanks Kids)