Perpendicular Waves: Exploring Interference in Overlapping Waves

[scijeebus]

If you have two waves overlapping each other which are perfectly perpendicular to each other, will there be any interference?

 

[mfb]

If the system is linear, you can always add the individual waves, independent of the angle and the amplitude of the waves, and independent of the number of different waves. The amplitude at a specific point+time is the sum of the amplitudes of the individual waves.

If the system is nonlinear, the waves might influence each other.

 

[scijeebus]

If the system is linear, you can always add the individual waves, independent of the angle and the amplitude of the waves, and independent of the number of different waves. The amplitude at a specific point+time is the sum of the amplitudes of the individual waves.

If the system is nonlinear, the waves might influence each other.

If I wave is oscillating in a specific direction x, and is not perpendicular to a different wave doing in direction y in 3-dimensional space (but let's say there's no friction that would cause the waves to lose energy over time), would there be destructive interference that would eventually cause the waves to die down?

 

[Philip Wood]

Everything is governed by the principle of superposition: at any point in the path of the waves, and at any time, the displacement is the vector sum of the displacements that each wave would give if it were the only wave. [This applies to linear systems, and most systems are linear unless the amplitude is very high.]

If the displacements of the individual waves are not at right angles, then their vector sum will depend on their phase difference, which will vary from one point to another, according to the difference in path length from the two sources (and the phases of the sources themselves). So there could be constructive or destructive interference, or something in between.

Destructive interference doesn't imply a dying down of waves over time. The amplitudes at each point won't change with time, as long as the sources go on emitting in the same way (same amplitudes and no discontinuities in their oscillations). Remember that if there is destructive interference at some points, there will be constuctive at others.

 

[scijeebus]

If the displacements of the individual waves are not at right angles, then their vector sum will depend on their phase difference, which will vary from one point to another, according to the difference in path length from the two sources (and the phases of the sources themselves). So there could be constructive or destructive interference, or something in between.

So are you implying if they are perpendicular their vector some will not be the phase difference and it would be a difference of something else or that they would not be summed?

 

[Philip Wood]

If they are perpendicular, there won't be constructive or destructive interference, but the resultant disturbance will still depend on the phase difference!

For example, if the component waves are each of amplitude A, and there is zero phase difference, the resultant disturbance will be in an oscillation in a straight line in a direction 'midway between' that of the component oscillations, and of amplitude [itex]\sqrt{2} A[/itex]. This is a simple consequence of the principle of superposition.

But if the component waves are out of phase by [itex]\tfrac{\pi}{2}[/itex], that is a quarter of a cycle, the particle in the medium will describe a circular path of radius A. Again, this follows from the principle of superposition.

Other phase differences will give elliptical paths.