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Give below are some functions of x and t to represesnt the displacement of an elastic wave. `(i) ``y=5cos (4x) sin (20t)` (ii) `y=4sin(5x-t//2)+3cos(5x-t//2)` (iii) `y=10cos[(252-250)pit]cos[(252+2500pit]` (iv)` y=100cos(100pit+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 Give reasons for your answers. |
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Answer» The four given equations are: (i) `y=5cos 4xsin20t` (ii) `y=4sin(5x-t//2)+3cos(5x-t//2)` (iii) `y=10cos(252-250)pit cos(252+250)pit` (iv) `y=100cos(100pit +0.5x)` From the basic concepts , we know (a) Eqn. (iv) represents a wave travelling along `-x` direction. (b) Eqn. (i) represents a stationary wave as terms containing x and t are independent. (c) Eqn. (iii) represents beats involving sum and difference of two frequencies 252 and 250. (d) Eqn. (ii) represents a wave travelling along `+x ` direction. |
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