Question

Which of the following statements are true for a stationary wave ?
A. Every paticle has a fixed amplitude which is different from the amplitude of its nearest particle
B. All the particles cross their mean position at the same time
C. There are some particles which are alwayss at rest
D. There is not transfer of energy across any plane

Answer 1

Correct Answer - A::B::D
Consider the equation of a stationary wave ` y= a sin (kx) cos omegat`
(a) clearly every paticle at x will have amplitude = a sin k x = fixed
(b) for mean position y=0
`rArr " " cos omegat=0`
`rArr " " omegat =(2n-1)(pi)/(2)`
Hence for a fixed value of n, all partice are having same value of
time `t=(2n-1)(pi)/(2omega)" "[because omega=` constant]
(c) amplitude of all the particles are a sin (kx) which isi different particles at different values of x
(d) the energy is a stationary wave is confined between two nodes
(e) particles at different nodes are always at rest.