The incident wave set up on a string of length fixed at each end is given by: y_1 =Asin(kx−wt) i)what is the equation of motion of the reflected wave,y_2 . ii)obtain the resultant,y=y_1 +y_2 of the two waves. iii)what type of resultant wave is this? iv)for what values of x will the amplitud of the resultant wave become zero? v)for what values of x will y be maximum?


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Question Number 38822 by NECx last updated on 30/Jun/18

$T h e i n c i d e n t w a v e s e t u p o n a s t r i n g$ $o f l e n g t h f i x e d a t e a c h e n d i s g i v e n$ $b y : y_{1} = A s i n (k x - w t)$ $i) w h a t i s t h e e q u a t i o n o f m o t i o n$ $o f t h e r e f l e c t e d w a v e, y_{2} .$ $i i) o b t a i n t h e r e s u l t a n t, y = y_{1} + y_{2}$ $o f t h e t w o w a v e s .$ $i i i) w h a t t y p e o f r e s u l t a n t w a v e i s$ $t h i s ?$ $i v) f o r w h a t v a l u e s o f x w i l l t h e$ $a m p l i t u d o f t h e r e s u l t a n t w a v e$ $b e c o m e z e r o ?$ $v) f o r w h a t v a l u e s o f x w i l l y b e$ $m a x i m u m ?$
Commented by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

	Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

	$i) y_{2} = A s i n (k x + w t)$ $i i) y_{1} + y_{2} = A s i n (k x - w t) + A s i n (k x + w t)$ $= 2 A s i n (k x) c o s w t$ $i i i) s t a n d i n g w a v e$ $i v) a m p l i t u d e = 2 A s i n k x$ $m a x a m p l i t u d e = 2 A m i n a m p l i t u d e = 0$ $w h e n s i n k x = 0 = s i n n Π$ $k x = n Π x = \frac{n Π}{k} = \frac{n Π}{2 Π} \times λ = n \frac{λ}{2}$ $v) m a x a m p l i t u d e = 2 A w h e n s i n k x = \pm 1$ $s i n k x = s i n (n + \frac{1}{2}) Π$ $k x = (n + \frac{1}{2}) Π$ $κ = \frac{2 Π}{λ}$ $2 \frac{Π}{λ} x = (n + \frac{1}{2}) Π$ $x = (n + \frac{1}{2}) \frac{λ}{2}$
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