If two waves have the same amplitude but different frequencies, their phase difference depends on the relative values of their frequencies and the specific time at which you compare them.
The phase difference between two waves is a measure of how much one wave is "shifted" or "offset" compared to the other wave. It is typically expressed in terms of degrees or radians.
When two waves have different frequencies, it means they complete their oscillations or cycles at different rates. Let's call the frequency of the first wave f1 and the frequency of the second wave f2, with f1 ≠ f2. The phase difference between them will depend on the ratio of their frequencies.
If the ratio of the frequencies is a rational number (expressible as a ratio of two integers), such as f1/f2 = m/n, where m and n are integers, then the waves will repeat their relative positions after a certain number of cycles. In this case, the phase difference will be a constant value, and you can calculate it based on the specific ratio of the frequencies.
For example, if the ratio of frequencies is 2:1 (f1/f2 = 2), it means that the second wave completes two cycles for every cycle of the first wave. In this case, the phase difference between them will be 360 degrees (or 2π radians) because the second wave completes a full cycle while the first wave completes half a cycle.
On the other hand, if the ratio of the frequencies is an irrational number (cannot be expressed as a ratio of integers), such as the ratio of π to e, then the waves will not repeat their relative positions after any finite number of cycles. In this case, the phase difference will continuously change and will not have a constant value.
In summary, if two waves have the same amplitude but different frequencies, the phase difference between them will depend on the ratio of their frequencies. If the ratio is rational, the phase difference will be a constant value, while if the ratio is irrational, the phase difference will continuously change over time.