Two sine waves that are very close to the same frequency (say, 0.5 Hz apart) will...

When two sine waves with frequencies that are very close together, such as 0.5 Hz apart, interact, they produce a phenomenon known as beating. This occurs because the two waves will constructively and destructively interfere with each other, resulting in an amplitude modulation over time.

As the two waves oscillate, their peaks and troughs will occasionally align, leading to moments of increased amplitude (constructive interference), followed by moments where they diminish each other (destructive interference). The frequency of this amplitude modulation, or the 'beat frequency,' is equal to the difference in frequency between the two waves—in this case, 0.5 Hz.

This beating effect can produce a rhythmic variation in sound or vibration, clearly evident when listening to musical instruments or observing vibration patterns. Understanding this concept is crucial in vibration analysis and helps in diagnosing issues related to machinery, where such frequency interactions may signify an imbalance or misalignment.