The transverse displacement of a string (clamped at its both ends) is given by y (x,t) = 0.06 sin (2πx/3) cos (120πt). All the points on the string between two consecutive nodes vibrate with

(a) Same frequency

(b) Same phase

(c) Same energy

(d) Different amplitude.

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, d) As we know by y (x, t) = 0.06 sin (2πx/3) cos (120πt)

By comparing the equation with general equation N denotes nodes and A denotes antinodes.

(a) Clearly frequency is common for all the points

(b) Consider all the particles between two nodes they are having same phase at given time

(c) But are having different amplitude of 0.06sin (2 $\frac{\pi }{3}x$ ) and because of different amplitudes they are having different energies.

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a, b, d) As we know by y (x, t) = 0.06 sin (2πx/3) cos (120πt)</p><p>By comparing the equation with general equation N denotes nodes and A denotes antinodes.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745487700phpDAFepS_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745487700phpDAFepS.jpeg" alt="" width="205" height="84"></picture></div></div><p> (a) Clearly frequency is common for all the points</p><p> (b) Consider all the particles between two nodes they are having same phase at given time</p><p> (c) But are having different amplitude of 0.06sin (2<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mi>x</mi> </math> </span>) and because of different amplitudes they are having different energies.</p>

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