A transverse harmonic wave on a string is described by y (x,t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right.

(a) The wave is travelling from right to left.

(b) The speed of the wave is 20m/s.

(c) Frequency of the wave is 5.7 Hz.

(d) The least distance between two successive crests in the wave is 2.5 cm.

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, c) y (x, t)=30sin (36t+0.018x+ $\frac{\pi }{4}$ )

Y=asin (wt+kx+ $\varnothing$ )

(a) as the equation involves positive sign with x . hence the wave is travelling from right to left. Hence option a is correct.

(b) W=36

2 $\pi v=36$

$v=\frac{36}{2\pi }$ = $\frac{18}{\pi }$

$k=0.018=\frac{2\pi }{\lambda }$

$\frac{2\pi v}{v\lambda }=0.018$

w/v=0.018

v=2000cm/s=20m/s

(c) 2 $\pi v=36$

$v=\frac{18}{\pi }$ = 5.7Hz

(d) $\frac{2\pi }{\lambda }=0.018$ , $\lambda =2\pi$ /0.0018cm=3.48cm

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a, b, c) y (x, t)=30sin (36t+0.018x+<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </mfrac> </math> </span>)</p><p>Y=asin (wt+kx+<span contenteditable="false"> <math> <mi>∅</mi> </math> </span>)</p><p> (a) as the equation involves positive sign with x . hence the wave is travelling from right to left. Hence option a is correct.</p><p> (b) W=36</p><p>2<span contenteditable="false"> <math> <mi>π</mi> <mi>v</mi> <mo>=</mo> <mn>36</mn> </math> </span></p><p><span contenteditable="false"> <math> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>36</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> </mfrac> </math> </span>=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>18</mn> </mrow> </mrow> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> </mfrac> </math> </span></p><p><span contenteditable="false"> <math> <mi>k</mi> <mo>=</mo> <mn>0.018</mn> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> </mfrac> </math> </span></p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>v</mi> <mi>λ</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.018</mn> </math> </span></p><p>w/v=0.018</p><p>v=2000cm/s=20m/s</p><p> (c) 2<span contenteditable="false"> <math> <mi>π</mi> <mi>v</mi> <mo>=</mo> <mn>36</mn> </math> </span></p><p><span contenteditable="false"> <math> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>18</mn> </mrow> </mrow> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> </mfrac> </math> </span>= 5.7Hz</p><p> (d) <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.018</mn> </math> </span>, <span contenteditable="false"> <math> <mi>λ</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> </math> </span>/0.0018cm=3.48cm</p><div><div><picture><img src="https://images.shiksha.com/mediadata/images/articles/1745487637phppbJ6Bh.jpeg" alt="" width="189" height="72"></picture></div></div>

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