15.13 Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:

(a) Y = 2 cos (3x) sin (10t)

(b) Y = 2

(c) Y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)

(d) Y = cos x sin t + cos 2x sin 2t

<p><strong> (a)</strong> The given equation represents a stationary wave because the harmonic terms kx and <span title="Click to copy mathml"><math><mi>ω</mi><mi>t</mi></math></span>&nbsp;appear separately in the equation.</p><p>&nbsp;</p><p><strong> (b)</strong> The given equation does not contain any harmonic term. Therefore, it does not represent either a travelling wave or a stationary wave.</p><p>&nbsp;</p><p><strong> (c)</strong> The given equation represents a travelling wave as the harmonic terms kx and <span title="Click to copy mathml"><math><mi>ω</mi><mi>t</mi></math></span>&nbsp;are in the combination of kx –&nbsp;<span title="Click to copy mathml"><math><mi>ω</mi><mi>t</mi></math></span> .</p><p>&nbsp;</p><p><strong> (d)</strong> The given equation represents a stationary wave because the harmonic terms kx and <span title="Click to copy mathml"><math><mi>ω</mi><mi>t</mi><mi></mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal"></mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">y</mi></math></span>&nbsp;in the equation. This equation represents the superposition of two stationary waves.</p>

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