The displacement of a string is given by y(x,t) = 0.06 sin (2πx/3) cos (120πt) where x and y are in m and t in s. The length of the string is 1.5m and its mass is 3.0× ${10}^{-2}\mathit{k}\mathit{g}$  .

(a) It represents a progressive wave of frequency 60Hz.

(b) It represents a stationary wave of frequency 60Hz.

(c) It is the result of superposition of two waves of wavelength 3 m, frequency 60Hz each travelling with a speed of 180 m/s in opposite direction.

(d) Amplitude of this wave is constant.

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (b, c) y (x, t) = 0.06 sin (2πx/3) cos (120πt)</p><p> (a) y (x, t)=asinkxcoswt</p><p> (b) w=120<span contenteditable="false"> <math> <mi>π</mi> </math> </span>, f=60hz</p><p> (c) k=2<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> </mfrac> <mi> </mi> <mo>, </mo> <mi> </mi> <mi>λ</mi> <mo>=</mo> <mn>3</mn> <mi>m</mi> <mo>, </mo> <mi> </mi> <mi>f</mi> <mo>=</mo> <mn>60</mn> <mi>h</mi> <mi>z</mi> </math> </span>, v =60 (3)=180m/s</p><p> (d) since in stationary wave all particles of the medium executes SHM with varying amplitude nodes.</p>

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