Actually, not only of the amplifier. The chart below allows you to automatically disconnect from the network any audio device with the absence at the output thereof sound for some time.
The scheme is powered by internal power supply of the device. Button S1 is turned on. Charge both capacitor, transistors open and relays and their contacts locks the button, leaving, thus, the device is in an enabled state. Further, the audio signal is the output signal of the amplifier or whatever you have is input to the transistor VT1 and it cannot be closed. In the absence of a signal at the output, the capacitors are discharged, the transistors are closed and the relay de-energizes the load. Temporary switch-off delay depends on the capacitance of the capacitors C1 and C2 and resistor R3. More than all this, the longer it will remain on the device when the absence of any signs of life at the output.
Publication: www.radiokot.ru, www.cxem.net