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  4. A wave travels in a medium according to the equation of displacement given by y( x, t) = 0.03 sin π (2t - 0.01 x) where y and x are in metre and t in second. The wavelength of the wave is

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Q. A wave travels in a medium according to the equation of displacement given by
$ y( x, t) = 0.03 \, \sin \pi (2t - 0.01 x) $
where $ y $ and $ x $ are in metre and $ t $ in second. The wavelength of the wave is

UPSEEUPSEE 2010Waves

Solution:

Comparing the given equation with standard wave equation we find that the propagation constant
$k =(\pi \times 0.01) m ^{-1}$
$\therefore $ Wavelength $\lambda =\frac{2 \pi}{k}$
$=\frac{2 \pi}{\pi \times 0.01}=200\, m$