Paragraph: Sinusoidal waves travel on five identical strings. Use the mathematical forms of the waves given below. In the expressions given below x is in m and y is in millimeters and t is in seconds. (a) y =(2 ~mm ) (2 x -4 t ) (b) y=(3 m m) (4 x-10 t) (c) y=(2.5 ~mm ) (6 x-12 t) (d) y=(1 m m) (8 x-16 t) (e) y=(4 m m) (10 x-20 t) Question: Two of the strings have the same energy in one wavelength, Identify the pair.

Step-by-step solution

(i) v ₁= w k = 4 2 =2 ~m / s aligned & v ₂= 10 4 =2.5 ~m / s & v ₃= 12 6 =2 ~m / s & v ₄= 16 8 =2 ~m / s & v ₅= 20 10 =2 ~m / s & v = T so T ₂ is diff. aligned aligned & (ii) E ₁= 1 2 vA ~A ^2 w ^2 ~T & 1 2 vA ~A ^2 4 f ^ t =2 v A ^2 ^2 f & E ₁=2 v 2^2 4 aligned aligned & E ₂=2 v 3^2 10 & E ₃=2 v 2.5^2 12 & E ₄=2 v 1^2 16 & E ₅=2 v 4^2 20 aligned So E ₁ & E ₄ are same (iii) slope BA ( kx - wt ) aligned & slope ₁=2 2 (2 8-4 4) & slope ₂=3 4 (6 8-10 4) & slope ₃=2.5 6 (6 8-12 4) & slope ₄=1 8 (8 8-16 4) & slope ₅=4 1