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  4. Two travelling waves produces a standing wave represented by equation, y =1.0 mm cos (1.57 cm -1) x sin (78.5 s -1) t The node closest to the origin in the region x>0 will bc at x = . cm

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Q. Two travelling waves produces a standing wave represented by equation,
$y =1.0 \,mm \cos \left(1.57 cm ^{-1}\right) x \sin \left(78.5 s ^{-1}\right) t$
The node closest to the origin in the region $x>0$ will bc at $x =$ ______.$ cm$

JEE MainJEE Main 2021Waves

Solution:

For node
$\cos \left(1.57 \,cm ^{-1}\right) x =0 $
$\left(1.57 \,cm ^{-1}\right) x =\frac{\pi}{2} $
$ x =\frac{\pi}{2(1.57)} \,cm =1 \,cm$