Physics simple question

Question

 1:- A particle moves in two SHM (simple harmonic motion) that have same vibrational direction and same frequency. The equation  of the two SHMs are given by X1= 4cos(wt+n/2)cm, x2= 10cos(wt-n/2)cm.  The amplitude of the additional (superposition) vibration is ?

A) 4cm;

B) 14cm;

C) 10cm;

D)6cm;

Answer 1

The 2 waves are out of phase by n/2-(-n/2)=n.  That suggests interference, but it depends on n.  For example, if n is a multiple of 2π, there is only constructive interference between the waves, and the amplitudes add up to 4+10=14.  But if n is an odd multiple of π, there is only destructive interference, and the amplitude drops to 10-4=6.  If n is neither a multiple of 2π or an odd multiple of π, the amplitude should be intermediate between 6 and 14.  I really do not think we can answer this question with a final number without knowing the value of n.  Is any other information provided in the original problem statement?