At a certain instant a stationary transverse wave is found to have maximum kinetic energy. The appearance of string at that instant is

Options

A. sinusoidal shape with amplitude `A/3`
B. sinusoidal shape with amplitude `A/2`
C. sinusoidal shape with amplitude `A`
D. straight line

Answer

a

Explanation

At instant `t = T//4 and t = 3T// 4,` the incident wave
travels a distance `3lambda//4` to the right and the reflected wave
travels the same distance on the string to the left. The
equivalent path difference between the waves is `lambda//2` or
`3lambda//2`. Therefore, crast of one wave fals on through of the
other and vice-versa. The resultant displacement at all
points is zero and is represented by thick horizontal line in
figure. Thus, all the particles are passing simultaneously
through their mean position, but in a direction opposite to
the direction at `t=T//4`.