Final answer:
An observer will hear silence due to destructive interference as two sound waves of the same frequency and amplitude cancel each other out when they are ½ wavelength out of phase.
Step-by-step explanation:
When two sound waves of exactly the same frequency and amplitude are produced by sources that are in precisely the same position, but are out of phase by one-half a wavelength, the observer standing a short distance away will experience destructive interference. This is because when the two waves are ½ wavelength out of phase, the crest of one wave aligns with the trough of another, leading to cancellation of the waves. this results in a total destructive interference and a resulting amplitude of zero, which implies that no sound will be heard by the observer.