SEMDI,
Thanks for replying with the additional details. They give us a great starting point as we isolate the Apple Music Radio issue. If it plays as expected with all other audio outputs and downloaded content, it sounds like you have nicely isolated the issue to only the speakers connected via the headphone jack and streaming content.
Since it only happens when you listen to Apple Music Radio, try troubleshooting your Wi-Fi connection first. This Apple Support article is a great resource when troubleshooting the Wi-Fi connection on your Mac:
Start with the basic preparations for Wi-Fi troubleshooting, and then follow the steps outlined in, "Symptom: The Wi-Fi network seems slow" and "Symptom: The network connection drops unexpectedly." They'll be the most relevant to your issue.
1. Does the symptom occur with more than one Wi-Fi device?
* Wi-Fi issues may be related to the network in question or they may be related to the Wi-Fi computer joining that network. Usually, if other computers or devices (such as Apple TV or iPhone) are able to get on the Internet without issues, then your Wi-Fi router is probably fine.
* If you only have one Wi-Fi device, proceed with this article.
2. Make sure your software is up to date.
* Install all software updates available for your Mac.
* If you use a third-party Wi-Fi router, check with the manufacturer to confirm that it has the latest firmware installed. If an update is available, follow the manufacturer's instructions for updating the firmware.
* To determine if your Apple Wi-Fi base station firmware is up to date, see Updating your software.
3. Check your connections.
* Some networking issues may be caused by loose or disconnected cables. Verify that all Ethernet and power cables connected between your modem and your Wi-Fi router are correct. Checking that devices such as your router and modem are on, disconnecting and carefully reconnecting Ethernet cables, and/or replacing damaged Ethernet cables may resolve the issue without any further troubleshooting.
4. Verify that you are using the recommended settings for your device.
* See Recommended settings for Wi-Fi routers and access points.
5. Restart your network devices.
* Powering your modem or router off for a few seconds and then on again may resolve network issues without any additional troubleshooting. If you have phone service through your ISP, power cycling your modem may interrupt that service. You may need to contact your ISP in order to restore your phone service if your modem is reset or powered off. Make sure that you have alternative means to contact your ISP (such as a cell phone) to avoid unnecessary delays in restoring your Internet or phone service.
If your Wi-Fi looks good, and you're able to stream Apple Music Radio using the built-in speakers for long periods of time, reach out to the manufacturer of your headphones to see if they have any recommendations.
Thank you for being part of the Apple Support Communities.
Kindest Regards.