Final answer:
To completely cancel a wave, add another wave with the same wavelength and amplitude but phase-shifted by 180°, resulting in destructive interference and a resultant amplitude of zero.
Step-by-step explanation:
To completely destroy a wave of a particular wavelength and amplitude, you need to add another wave with the same wavelength and amplitude but with a phase change of 180°, or π radians. This is because when two waves are exactly out of phase by a half-wavelength, they undergo destructive interference, resulting in a new wave of zero amplitude. Therefore, to achieve this, you must ensure that the second wave you add has the same wavelength and amplitude as the existing wave, but with a phase difference of 180°.