What defines beat frequency in wave interference?

Beat frequency occurs when two waves of slightly different frequencies interfere with each other. When these waves combine, they create a new wave pattern characterized by periodic variations in amplitude, known as beats. The frequency of these amplitude variations is determined by the difference between the frequencies of the two original waves.

Thus, when you have two waves with frequencies (f_1) and (f_2), the beat frequency is given by (|f_1 - f_2|). This means that if you were to plot the resulting wave, you would observe oscillations that occur at a rate equal to the difference in frequencies. Such a behavior forms the basis of various applications in sound synthesis and acoustics, where beating effects are often exploited creatively.

In this context, the other options do not characterize the beat frequency correctly, as the average or sum of the frequencies does not produce the characteristic beat pattern, nor does the amplitude of the waves determine the beat frequency itself.