When you add two sine waves with different frequencies (or periods) together, the result is a new wave that exhibits a phenomenon known as "beat" or "beat frequency." This effect occurs due to the interference between the two waves.
The resulting waveform is characterized by a pattern of alternating constructive and destructive interference. Constructive interference happens when the peaks of the two waves align, resulting in an amplitude that is the sum of the individual amplitudes. Destructive interference occurs when the peaks of one wave align with the troughs of the other, leading to a cancellation of amplitudes.
The beat frequency is the difference between the frequencies of the two original sine waves. Let's say you have two sine waves with frequencies f1 and f2, where f1 > f2. The beat frequency (fbeat) can be calculated as:
fbeat = |f1 - f2|
The beat frequency represents the rate at which the amplitude of the resulting waveform varies. The amplitude of the resulting wave oscillates at this beat frequency. The slower the beat frequency, the more perceptible the oscillations will be to the human ear.
If the frequencies are relatively close to each other, you will observe a slow modulation in the amplitude of the resulting wave. As the frequencies become closer, the beat frequency decreases, resulting in a slower variation in amplitude. Conversely, if the frequencies are significantly different, the beat frequency will be higher, leading to a faster variation in amplitude.
This beat phenomenon is commonly encountered in various contexts, such as music, sound engineering, and physics experiments. It provides a useful tool for analyzing and manipulating waveforms with different frequencies.