Principle of Superposition of Waves

Light waves each of amplitude "a" and frequency "ω", emanating from two coherent light sources superpose at a point. If the displacements due to these waves are given by y₁ = a cos ωt and y₂ = a cos(ωt + ϕ) where ϕ is the phase difference between the two, obtain the expression for the resultant intensity at the point.

Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for

If `sqrt("A"^2+"B"^2)` represents the magnitude of resultant of two vectors `(vec"A" + vec"B")` and `(vec"A" - vec"B")`, then the angle between two vectors is ______.

In the interference of two sources of intensities I₀ and 9I₀ the intensity at a point where the phase difference is `pi/2` is ______.

For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of What is the phase difference between the oscillation of a particle located at x = 100 cm, at t = T s and t = 5 s?

For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of `λ/2`

When two coherent monochromatic light beams of intensities I and 4I are superimposed, then what are the maximum and minimum possible intensities in the resulting beams?

For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of `(3λ)/4` (at a given instant of time)