Phase difference is the angular difference between two sinusoidal waveform of the same frequency. It tells us how much one wave is “ahead of” or “behind” another in terms of their cycles
The word phase in normal usage means any stage in a series of events or in a process of development.
Cambridge University dictionary defines phase as one of the stages or points in a repeating process measured from a specific starting point.
Two Waves can be of the same amplitude but with the different frequencies as shown in figure below.
The wave profile P makes it’s one complete oscillations before wave Q. Wave P has shorter wavelength compared to Q and hence P has higher frequency.
We can also see that P has smaller period as waves with shorter wavelength has smaller period.
Wave P completes it’s first cycle at A while Q finishes it’s first oscillation at B. We can say that P is leading Q. The maximum displacement of the two waves is the same hence they are operating at the same amplitude but different frequency. The two waves are said to be out of phase. Think about two radio receivers tuned to two different stations but with equal volume.
waves can also be of the same frequency but different amplitudes. Think of when we tune in our two radio receivers to the same station and then set them at different volumes
The figure below illustrates two waves operating at same frequency but at different amplitudes.
One wave is having more displacement than the other. However, they are arriving at the horizontal position simultaneously, as can be seen from the diagram. We say they are in phase.
Pendulum bobs in phase
To further illustrate the concept of phase and out of phase oscillations, consider two identical pendulums. The pendulums have bobs P and Q below.
We set the two masses, P and Q in oscillation. We give them some displacement on the left and then releasing them simultaneously. They have equal displacement because we have released at the same time. Therefore, they will pass through the lowest point Y simultaneously as they move in the opposite direction. They attain displacement together at Z and swing back together to complete the oscillation at x.
At any particular moment, the two masses will be moving in the same direction. They will also be at the same level of displacement in their oscillation. We say that the masses are oscillating in phase.
particles in phase difference
When particles in a wave motion happens to be oscillating in the same direction and at the same level of displacement, we say that their oscillation are in phase.
The diagram below have highlighted two positions of particles A and B. The particles are at the same displacement level from the reference line. They are both facing the same direction as indicated by the arrows. The particles A and B are said to be in phase and their distance apart is the wavelength λ of the wave motion whereas time taken to move from A to B is the periodic time T.
Particles in a wave motion can be in phase even if they have different amplitude.
In our previous pendulum oscillation of mass P and Q ; If P is Initially given a larger displacement than Q, the two will oscillate in phase. However, P will always be at a larger magnitude of displacement than Q.
A typical displacement time graph for two wave motions in phase with different amplitudes is shown below.
Oscillations out of phase
Consider two masses P and Q displaced from opposite directions from each other as in figure below.
When released simultaneously, they pass through the rest position at the same time. They move in opposite directions. They reach a point of maximum displacement at the same time. However, their maximum displacement is in opposite directions to each other.
Waves 180o out of phase difference
The two objects above are always at the opposite levels of displacement and their oscillations opposite direction to each other and they are said to be in opposite phase.
Wave motions that have same displacement and makes complete oscillations at the same time with their maximum displacements in exact opposite to each other are said to be in 180o phase difference (180o out of phase).
The figure below shows two wave motions at 180o phase difference.
Waves 90o out of phase difference
suppose in our pendulum oscillations we displaces the objects P and Q to X ; we release Q before P and then we release p when Q is exactly at Y. The angle of oscillation between P and Q will be 90o in difference and the resulting oscillation will be 90o out of phase.
The displacement time graph for waves 90o out of phase is illustrated below.
two waves can be out of phase at any angle. We are to see that in our future lessons.