Given below are some functions of x and t to represent the displacement of an elastic wave.

(a) y = 5 cos (4x ) sin (20t)

(b) y = 4 sin (5x – t/2) + 3 cos (5x – t/2)

(c) y = 10 cos [(252 – 250) πt ] cos [(252+250)πt ]

(d) y = 100 cos (100πt + 0.5x )

State which of these represent

(a) A travelling wave along –x direction

(b) A stationary wave

(c) Beats

(d) A travelling wave along +x direction.

Given reasons for your answers.

<p><span data-teams="true">This is a long answer type question as classified in NCERT Exemplar</span></p><p><strong> (a)</strong> The equation y = 100 cos (100πt + 0.5x ) is representing a travelling wave along x-direction</p><p><strong> (b) </strong>The equation y = 5 cos (4x ) sin (20t) represents a stationary wave, because it contains sin cos terms ., combinations of two progressive waves.</p><p><strong> (c) </strong>The equation y = 10 cos [ (252 – 250) πt ] cos [ (252+250)πt ] involving sum and difference of two near by frequencies 252 and 250 have this equation represents beats formation.</p><p><strong> (d) </strong>As the equation y = y = 4 sin (5x – t/2) + 3 cos (5x – t/2) involves negative sign with x, have if represents a travelling wave along x – direction.</p>

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