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

(a) Every particle 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) All the particles are oscillating with same amplitude.

(d) There is no net transfer of energy across any plane.

(e) There are some particles which are always at rest.

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a, b, d, e) a) clearly every particle at x will have amplitude =asinkx=fixed</p><p>b) for mean position =0</p><p>coswt=0</p><p>wt= (2n-1)<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>hence for a fixed of n all particles are having same value of time t= (2n-1)<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>w</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>c) amplitude of all the particles are asinkx which is different for different particles at different values of x</p><p>d) the energy is a stationary wave is confined between two nodes.</p><p>e) particles at different nodes are always at rest.</p>

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