Just as you quoted from the documentation, starting a tool does not start the selected output device, so you need to tell the appropriate device to start.

Here's a sample script that picks the first available output device on the system, and outputs a 1 kHz tone on that device:

tell application &quot;Electroacoustics Toolbox&quot;
	activate
	create new project
	set devList to name of devices
	
	-- make sure there is at least one device connected to the system
	if (count of devList) is greater than 1 then
		-- make sure there is at least one device with output channels connected to the system
		-- pick the first output device found
		set foundOutputDevice to false
		repeat with i from 1 to count of devList
			set dev to device (item i of devList)
			if (count of output channels of dev) is greater than 0 then
				set foundOutputDevice to true
				exit repeat
			end if
		end repeat
		
		if foundOutputDevice then
			set sigGen to make new signal generator tool with properties {id:&quot;siggen&quot;}
			tell sigGen
				set selected device to dev
				set periodic signal A enabled to true
			end tell
			tell dev to start
			tell sigGen to start
		else
			display dialog &quot;There are no devices with output channels available on your system. Please connect an audio output device and try again.&quot;
		end if
	else
		display dialog &quot;There are no devices available on your system. Please connect an audio device and try again.&quot;
	end if
end tell