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  • A wave is represented by <img alt="y = 20\sqrt{3} \sin (\frac{2\pi t}{T} - \frac{2\pi x}{\lambda})" src="https://entrancecorner.oncodecogs.com/gif.latex?y%20%3D%2020%5Csqrt%7B3%7D%20%5Csin%20%

A wave is represented by y = 20\sqrt{3} \sin (\frac{2\pi t}{T} - \frac{2\pi x}{\lambda}) cm. The displacement of a particle at the position x = \frac{\lambda}{6} on the wave at time t = \frac{T}{3} is:

Option: 1

30 cm


Option: 2

40 cm


Option: 3

50 cm


Option: 4

60 cm


Answers (1)

best_answer

In the given equation:

y = 20\sqrt{3} \sin (\frac{2\pi t}{T} - \frac{2\pi x}{\lambda})

Putting x = \frac{\lambda}{6}  and t= \frac{T}{3}, we get:

displacement, 

y = 20\sqrt{3} \sin (\frac{2\pi T}{3T} - \frac{2\pi \lambda}{6\lambda})

    = 20\sqrt{3} \sin (\frac{2\pi}{3} - \frac{\pi}{3})

    = 20\sqrt{3} \sin \frac{\pi}{3}

    = 20\sqrt{3} \cdot \frac{\sqrt{3}}{2}

    = 30 cm

Posted by

Nehul

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