Striking two adjacent keys on a piano produces a warbling combination (usually considered unpleasant to the ear). The culprit is the superposition of two waves of similar but not identical frequencies. When two waves of similar frequency arrive at the same point and superimpose, they alternately constructively and destructively interfere. This alternating is known as a beat because it produces an unpleasant pulsing sound.
Another example is often noticeable in a taxiing jet aircraft (particularly the two-engine variety). The loudness of the combined sound of the engines increases and decreases. This varying loudness occurs because the sound waves have similar but not identical frequencies. The discordant warbling of the piano and the fluctuating loudness of the jet engine noise are both due to alternately constructive and destructive interference as the two waves go in and out of phase. illustrates this phenomenon graphically.
Beat Frequency
Beats are produced by the superposition of two waves of slightly different frequencies but identical amplitudes.The waves alternate in time between constructive interference and destructive interference, giving the resulting wave a time-varying amplitude.
The wave resulting from the superposition of two similar-frequency waves has a frequency that is the average of the two. This wave fluctuates in amplitude, or beats, with a frequency called the beat frequency. We can determine the beat frequency mathematically by adding two waves together.
One can also measure the beat frequency directly. When you hear a beat coming from two discordant sounds (say, two notes on a piano) you can count the number of beats per second. The number of beats per second, or the beat frequency, shows the difference in frequency between the two notes. Musicians often use this phenomena to ensure that two notes are in tune (if they are in tune then there are no beats).