If you use an active piezo buzzer, it has the circuitry to generate an audible frequency built in to the buzzer so all you need to do to get a beep is set the output pin HIGH. Most of the piezo buzzers that are in an enclosure (rather than just the bare piezo discs) are active.
But I must get some kind of audible tones at that clock speed, just a couple of audible beeps.
You can. If you don't mind blocking code simply write successive zeros and ones to a pin in a tight loop. As digitalWrite has such a high overhead in terms of clock cycles then use direct port addressing to make the tones in the audible region.
back and forth many times?
How do you alter the tone from one pitch to another?