When two sinusoidal waves have the same amplitude but different frequencies, the phase difference between them depends on the relative rates at which they complete their cycles.
Let's assume we have two sinusoidal waves:
Wave 1: A1 * sin(2πf1t + φ1) Wave 2: A2 * sin(2πf2t + φ2)
where A1 and A2 represent the amplitudes of the waves, f1 and f2 represent their respective frequencies, t represents time, and φ1 and φ2 represent the phase offsets.
The phase difference, denoted as Δφ, can be calculated as:
Δφ = (2πf1t + φ1) - (2πf2t + φ2)
Simplifying the expression, we have:
Δφ = 2π(f1 - f2)t + (φ1 - φ2)
From this equation, we can see that the phase difference between two sinusoidal waves of the same amplitude but different frequencies will vary linearly with time. The term (2π(f1 - f2)t) represents the changing phase difference due to the difference in frequencies, and (φ1 - φ2) represents any initial phase difference between the waves.
It's important to note that the phase difference will continue to change over time due to the different rates at which the waves complete their cycles.