Yes, it is possible to have two different amplitude sine waves that are in phase with each other. Mathematically, this can be represented as:
Wave 1: A₁ sin(ωt) Wave 2: A₂ sin(ωt)
In this representation, A₁ and A₂ are the amplitudes of the two waves, ω is the angular frequency, and t represents time. Both waves have the same angular frequency and are in phase, which means that their crests and troughs occur at the same points in time.
The amplitudes A₁ and A₂ can be different, which implies that the magnitudes or intensities of the two waves are not equal. The phase difference between the two waves in this case is zero, indicating that they are perfectly aligned in time.
Visually, if you were to graph these two waves on a coordinate plane with time on the x-axis and displacement (or amplitude) on the y-axis, you would observe two sine waves that have different amplitudes but reach their maximum and minimum values simultaneously. The waves would be in phase, sharing the same starting point and exhibiting the same pattern of oscillation, but with different magnitudes.
It is important to note that the superposition of these two waves will result in a new wave with an amplitude equal to the sum of the individual amplitudes. This principle is known as the principle of superposition, which states that the displacement of a medium caused by the interference of two or more waves is the algebraic sum of the individual displacements at each point in space and time.