Two sinusoidal waves of identical frequency travel in the same direction along a stretched string. Each has amplitude A and there is a constant phase difference θ between them.
(i) State the principle of superposition of waves.
(ii) Without performing any algebraic derivation, write an expression for the resultant displacement produced by the two waves at any instant. Clearly define each symbol used.
(iii) Explain qualitatively how the resultant amplitude depends on the phase difference θ.
(iv) Identify the values of θ for which the waves (a) reinforce each other completely and (b) cancel each other completely. Give a brief reason for each case.