Two sound waves of the same frequency travel in the same direction through still air. The first wave has displacement amplitude A1 while the second has displacement amplitude A2. The phase of the second wave leads that of the first by a constant angle ϕ.
(i) Write an expression for the resultant displacement at any instant when the two waves overlap.
(ii) Derive an expression for the resultant amplitude A in terms of A1, A2 and ϕ.
(iii) Using your result, obtain expressions for (a) the maximum possible intensity and (b) the minimum possible intensity in terms of A1 and A2.
(iv) If A1=3mm and A2=4mm, calculate the ratio of the maximum intensity to the minimum intensity.