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  • Two waves, <img alt="y_1=A \sin (\omega t-k x) \text { and } y_2=A \sin (\omega t+k x)" src="https://entrancecorner.oncodecogs.com/gif.latex?y_1%3DA%20%5Csin%20%28%5Comega%20t-k%20x%29%20%5C

Two waves,
y_1=A \sin (\omega t-k x) \text { and } y_2=A \sin (\omega t+k x)
superimpose to produce a stationary wave, then 

Option: 1

x = 0  is a node


Option: 2

x = 0  is an antinode


Option: 3

x=\frac{\pi}{k}   is a node.


Option: 4

x=\frac{2 \pi}{k}  is an antinode.


Answers (1)


y=y_1+y_2 =(2 A \cos k x) \sin \omega t \\

=A_x \sin \omega t

Here, A_x=2 A \cos k x

At  t=0, Ax is maximum or  2 A

So, it is an antinode. Next antinode will occur at  x=\frac{\lambda}{2}, \lambda, \ldots, etc

x=\frac{\pi}{k}, \frac{2 \pi}{k}, \ldots ., etc .
 

 

Posted by

Kshitij

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