(i) A sinusoidal wave is travelling along positive x direction and the displacements at two positions `x = 0` and `x = 1 m` are given by `y (0, t) = 0.2 cos (3 pi t)` and `y(1, t)=0.2 cos (3pit+pi/8)` Find all possible wavelength of the wave if it is known that wavelength is greater than 0.4 m.
(ii) A transverse sine wave of amplitude `a = 0.1 cm` is travelling along a string laid along the x-axis. The displacement (y) – time `(t)` graph of the string particle at `x = 0.1 m` is shown in first figure. The shape of the string at time `t = 0.1 s` is shown in second figure. At this time the particle at `x = 0.11 m` is having velocity in positive y direction write the equation of wave.

Answer

(i) `16/15 m` and `16/31 m`
(ii) `y=(0.1 cm) cos [(20 pi m^(-1) x]+(10 pi s^(-1))t]`