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  • The expression for a standing wave is <img alt="y (x,t) = 2 \sin (0.1 \pi x) cos 100\pi t" src="/latex-image/?y%20%28x%2Ct%29%20%3D%202%20%5Csin%20%280.1%20%5Cpi%20x%29%20cos%20100%5Cpi%20t" /

The expression for a standing wave is y (x,t) = 2 \sin (0.1 \pi x) cos 100\pi t, where x and y are in cm and t is in second. Then the distance between a node and the next antinode of the wave is:

Option: 1

6 cm


Option: 2

5 cm


Option: 3

4 cm


Option: 4

10 cm


Answers (1)

best_answer

y (x,t) = 2 \sin (0.1 \pi x) cos 100\pi t

                = a \sin kx \cos \omega t

Here, 

k = 0.1 \pi , \omega = 100\pi

\implies \lambda = \frac{2\pi }{k} = \frac{2\pi }{0.1\pi } = 20 cm

So, the separation between a node and the next antinode is:

\frac{\lambda}{4} = \frac{20}{4} = 5 cm

Posted by

Divya Prakash Singh

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