When two harmonics are added together, the resulting wave is a combination of both waves. The behavior of the frequency and amplitude depends on the specific characteristics of the harmonics being added.
Frequency:
If the two harmonics have the same frequency, their addition will result in a wave with the same frequency as the original harmonics. The frequency remains unchanged.
If the two harmonics have different frequencies, the resulting wave will have a frequency that is determined by the combination of the original frequencies. This is known as the principle of superposition. The resulting wave will exhibit a beat frequency, which is the difference between the frequencies of the two original waves. The beat frequency is heard as a variation in amplitude, producing a pulsating or "beating" effect.
Amplitude:
If the amplitudes of the two harmonics being added are of the same sign and similar magnitudes, the resulting amplitude will be larger. This is known as constructive interference, where the amplitudes add up.
If the amplitudes of the two harmonics are of opposite signs or significantly different magnitudes, the resulting amplitude will be smaller. This is known as destructive interference, where the amplitudes partially or completely cancel each other out.
In summary, when harmonics are added together, the resulting wave's frequency can remain the same or be influenced by the combination of the original frequencies. The amplitude can be larger (constructive interference) or smaller (destructive interference) depending on the relative amplitudes of the harmonics being added.