Blackmoor Vituperative

I have a 2023 Mustang GT with the 9-speaker setup but no subwoofer. My intention is to replace the speaker, add an amp, and wire it into the back speakers using the same method as shown in this YouTube video:

https://youtu.be/XxNDhOutHzw?si=LwDcEGA_EOq7Vyls

My current parts list includes:

• Rockford Fosgate R500X1D Prime 1-Channel Class D Amplifier
• Pioneer TS-A250D4 10″ Dual 4 ohms Voice Coil Subwoofer, Black
• Skar Audio 4 Gauge Amplifier Wiring Kit – Blue, Copper Clad Aluminum, SKAR4ANL-CCA

l think these are these good choices for this purpose, but I am still doing research. My intention is to keep it under $400, not including the enclosure (which was $175 delivered).

I have never installed a sub in a system without a dedicated output for the sub. I might need some kind of audio high-pass/low-pass splitter between the rear deck speaker wires and everything else. An amateur-friendly one, I hope.