The resultant wave will have an amplitude √2a (Option B).
How to calculate the amplitude of the resultant wave?
The amplitude of the resultant wave is calculated by applying the following formula as shown below.
y₁ = a sin(ωt - kx)
y₂ = a cos(ωt - kx)
The resultant wave after the superposition is obtained by adding the two displacements.
y₁ + y₂ = a sin(ωt - kx) + a cos(ωt - kx)
Using trigonometry identity of;
sin θ + cos θ = √2 sin (θ + π/4)
If we apply the trigonometry identity in summing the displacements of the waves, we will have;
a sin(ωt - kx) + a cos(ωt - kx) = a√2 sin (ωt - kx + π/4)
The general equation of wave of wave is;
y = A sin(ωt - φ)
The amplitude, A corresponds to;
A = a√2