Two waves are represented by y_1 =Asinωt and y_2 =Asin(ωt−δ). What is the resultant of the two waves? ii)determine the amplitude of the resultant wave and under which condition will it be constructive or destructive.


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Question Number 38816 by NECx last updated on 30/Jun/18

$T w o w a v e s a r e r e p r e s e n t e d b y$ $y_{1} = A s i n ω t a n d y_{2} = A s i n (ω t - δ) .$ $W h a t i s t h e r e s u l t a n t o f t h e t w o$ $w a v e s ?$ $i i) d e t e r m i n e t h e a m p l i t u d e o f t h e$ $r e s u l t a n t w a v e a n d u n d e r w h i c h$ $c o n d i t i o n w i l l i t b e c o n s t r u c t i v e o r$ $d e s t r u c t i v e .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

	$y_{1} + y_{2} = 2 A s i n (w t - \frac{δ}{2}) c o s (\frac{δ}{2})$ $a m p l i t u d e = 2 A c o s (\frac{δ}{2})$ $c o n s t r u c t i v e w h e n c o s (\frac{δ}{2}) = \pm 1$ $c o s (\frac{δ}{2}) = c o s (n Π)$ $δ = 2 n Π$ $d e s t r u c t i v e w h e n c o s (\frac{δ}{2}) = 0 = c o s (n \frac{Π}{2})$ $δ = n Π$
	Commented by NECx last updated on 30/Jun/18

	$w o w . . . . . T h a n k y o u s o m u c h .$
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