Physics travelling waves

Question

Two counter-propagating waves of amplitude A, wave number k and angular frequency w
and equal initial phase excite a standing wave on a string of mass per unit length 3 g m-1
which placed under a tension of 78 N. The standing wave is described by the equation
y(x,t) = 2Asinkxcoswt.

 

The initial phase of one of the component waves is changed by π/2 radians. Why do the
positions of the nodes change (3 marks)

 

Determine the relative change in position of one of the
nodes on the string? (5 marks)

 

I don't know what to say for either of these questions. Help would be appreciated

Answer 1

   Due to the addition of the phase, the new standing wave equation is y(x,t)=2Asin(kx±π/4)cos(ωt±π/4).  The sign depends whether the phase is negative or positive.  You can get this by using the trigonometric identities 2sinθcosφ=sin(θ+φ)+sin(θ-φ) and sinθ+sinφ=2sin(θ/2+φ/2)cos(θ/2-φ/2).