Where does the sound come from?
Air from his/her extended trunk.
Source, hours and hours of National Geographic and Wild Kingdom. I’ve seen them do it.
They are quite noisy.
They can only produce a few notes because their fingers are too big for the valves.
How do you talk?
Air from the animals’ lungs pass quickly through a fenestrated membrane in the airway path, making a sound. The fenestrated membrane can be different in different animals.
I’m still waiting to hear them whistle. 
Lauren Bacall — ‘If you want me just whistle. You know how to whistle don’t you? Just put your lips together and blow.’
I wondered if the sinus cavities were involved, too, but maybe it’s just a matter of how fast or slow the air passes through the trunk .Here’s an article about how they produce different sounds. Elephants make a fascinating variety of noises, and much of their communication is actually done below the range of human hearing. An elephant’s infrasonic rumbles can travel a great, great distance along the ground, and other elephants feel them with their feet rather than their ears.
The trunk isn’t the only end where sound comes out.
Trust me on this, don’t ever stand behind an elephant.
So, essentially, an elephant’s trumpeting is the sound of it blowing its nose?
…and why can’t a trumpet “elephant”?
Are these two answers both true? Are they consistent with one another?
That’s what I first thought but now I’m thinking it works kinda like the gyrations our bodies go through to generate a sound we blow a fart. Guess we’ll just have to wait until a pachydermiologist replies to this thread.
I hate to think what its handkerchief must be like!