When two sinusoidal waves with equal amplitudes and phases but different frequencies are superimposed on each other, the resulting waveform will exhibit a phenomenon known as beat interference.
The resulting waveform will have a frequency equal to the difference between the frequencies of the two original waves. This is known as the beat frequency. Mathematically, if the frequencies of the two waves are f₁ and f₂ (where f₁ > f₂), then the beat frequency (f_beat) can be calculated as:
f_beat = |f₁ - f₂|
The beat frequency represents the rate at which the amplitude of the resulting waveform varies. It will be equal to the absolute difference between the frequencies of the original waves.
The amplitude of the resulting waveform will vary sinusoidally with time, following the beat frequency. The amplitude will be modulated, with the envelope of the resulting waveform exhibiting an oscillatory pattern. The amplitude of this envelope will be equal to the average of the amplitudes of the original waves.
In summary, when two sinusoidal waves with equal amplitudes and phases but different frequencies are superimposed, the resulting waveform will have a beat frequency equal to the difference between the original frequencies. The amplitude of the resulting waveform will vary sinusoidally with time, with the envelope of the waveform representing the average amplitude of the original waves.