Which of the following statements are true for a stationary wave ?

Options

A. (A) Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
B. (B) All the particles cross their mean position at the same time.
C. (C) All the particle are oscillating with same amplitude.
D. (D) There is no net transfer of energy across any plane.

Answer

A, B, D

Explanation

(a) In case of stationary wave, amplitude of oscillation of a particle at distance x from one end is `A. = 2 a sin (kx)`
For A given particle x = constant
A.= constat
For neightbouring particle, x is slightly different . Hence , their amplitudes are also slightly different. Thus, option (A) is true.
(b) Here frequency f is same for all the particles. Hence, T is same for all the particles and so `T/2` is also same which is time to pass through the respective mid point. Thus, option (B) is true.
(c) All the particles do not have same ampli tudes because here amplitude of any given particle depends on its position according to formula A. = 2a sin(kx). Thus, option © is false.
(d) In case of stationary wave, there is no trans fer of energy because the entire length of medium becomes an isolated system which does not interact with the surrounding. Thus, option (D) is true.
(e) At all the nodal points, particles of medium remain at rest at all the times. Thus, option (E) is true.