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The vibrations of a string of length 60 cm at both ends are represented by the equation. y =4 sin[(pix)/(15)] cos (96 pi t) where x and y are in cm and t is in sec. Write down the equations of component waves whose superposition gives the above wave. |
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Answer» Solution :As `2 sin A cos B = sin (A +B) + sin (A -B)` So `y = 4sin [(PI x)/(15)] cos (96PI t)` `=2[sin((pi x)/15 + 96pi t) + sin ((PIX)/15 -96pit)]` ` y = 2sin [96pit+(pi x)/15] - 2 sin [96 pi t - (pix)/15]` `[as sin(-theta) = - sintheta]` `y = y_1 + y_2" with" y_1 = 2sin [ 96pi t +(pix)/(15)]` `y_2 = -2 sin [96 pi t - (pi x)/15]` |
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