When a string vibrates in its second mode (also known as the second harmonic or first overtone), it indeed has two halves that vibrate in opposite directions. This can create the impression of an out-of-phase shift and potential destructive interference. However, it is important to note that the sound produced by a vibrating string is not the result of interference between the two halves of the string.
The primary mechanism by which a vibrating string creates sound is by displacing the surrounding air particles. As the string moves back and forth, it creates alternating regions of compression and rarefaction in the air, which result in the formation of sound waves. These sound waves then propagate through the air as longitudinal pressure waves and reach our ears, where they are perceived as sound.
The fact that the string has two halves vibrating in opposite directions does not lead to significant destructive interference in terms of the sound wave itself. The individual contributions from each half of the string combine to form the resulting sound wave. The specific pattern of the string's vibration, determined by its mode of vibration, determines the frequency and quality of the sound produced.
It's worth noting that interference phenomena, such as destructive interference, can occur in the context of sound waves, but they typically involve the interaction of multiple sound sources or the reflection of sound waves. However, in the case of a vibrating string producing sound, the focus is primarily on the displacement and compression of air particles rather than interference between different parts of the string.