Trying to identify a jack similar to, but different from, a 1/8 headphone jack

The rings on a audio jack indicate the number of channels it supports. The below image shows the common types of jacks 

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Since your jack has only one ring it means it is a monochannel audio jack, you can use the term to find one in your electronics shop or even use a jack that has two rings. If you are using the one with two rigns the you have to ignore one wire on the output side since your system will support only monochrome audio. You can use a multimeer to check for continuity and identitfy which wires corresponds to which sleeve 

There are two commonly used audio jacks in the audio projects, one of those are 3.5mm jack while the other one is 6.8mm jack. I don't know which one you want to get. But to get your required one, which contains only one black ring, commonly known as mono audio jack, which you can easily find in the local electronics market. If you want to get some technical support regarding your audio development projects, you can visit the SSLA platform for getting better assistance.

There are two commonly used audio jacks in the audio projects, one of those is a 3.5mm jack while the other one is a 6.8mm jack. I don't know which one you want to get. But to get your required one, which contains only one black ring, commonly known as mono audio jack, which you can easily find in the local electronics market. If you want to get some technical support regarding your audio development projects, you can visit the Sierra Software Ltd. platform for getting better assistance.