The "stages" of this project are:

1. Smartphone connected to wifi
2. Old audio amplifier (pc speakers or bluetooth speaker)
3. Comparator and relay circuit (made by you!)

The objective is to energize the relay to switch anything (in this case to connect the two wires that signal the garage door opener)

First you need to locate the output of your audio amplifier and remove any bootstrap or filter capacitors connected to it. You should see about 3V DC when the sound is not playing and about 5V DC when the sound is playing. Remove the speaker connection as well so that all the current goes to the comparator input.

Find the ground on your amplifier and connect it to ground on your protoboard with your 5V source.

Construct the simple LM311 comparator from http://www.learningaboutelectronics.com/Articles/LM311-voltage-comparator-circuit.php

Instead of connecting an LDR and the 33K resistor, connect only the speaker output of the amplifier after removing the speaker itself and the capacitors.

Instead of an LED in the output, connect the coil of the RAS0510. No resistor is needed.

Play a loud sound on the amplifier using the old smartphone and make sure the coil on the relay is energized (you can use an LED on the common and NC pins).

Turn off the sound and make sure the coil is not energized. If it is, rotate the potentiometer until it turns off and test again.

I used the WIFI Talkie app on android to send a message and setup a really loud notification to trigger the comparator.

https://play.google.com/store/apps/details?id=com.remaller.android.wifitalkie&hl=en

Use this app to make sure the notification plays on the amplifier and not in the phone's internal speaker - SOUNDABOUT

https://play.google.com/store/apps/details?id=com.woodslink.android.wiredheadphoneroutingfix&hl=en

Check out the simulation on 123D

https://123d.circuits.io/circuits/1586781-reuse-garage-door-opener

The simulation is done with LM741 instead of LM311 that I really used. Same principle.

If you follow the 123D circuit remove the slideswitch and connect the output of your sound amplifier to the negative input of the opamp

Extra points: You can use an LM7805 to create your VCC and use the same voltage source as the amplifier to power the smartphone, comparator and realy!