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  4. When a wave travels in a medium the particles displacement is given by the equation y=0.03 sin π(2 t-0.01 x), where x and y are in seconds. The wavelength of the wave is :

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Q. When a wave travels in a medium the particles displacement is given by the equation $y=0.03 \sin \pi(2 t-0.01 \,x)$, where $x$ and $y$ are in seconds. The wavelength of the wave is :

BHUBHU 2003

Solution:

Compare the given wave equation with its similar standard wave equation.
The standard wave equation is
$y=a \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right) \,\,\,...(1)$
Where $a$ is amplitude,
$T$ is periodic time and $\lambda$ is displacement.
Given, equation is
$y=0.03 \sin \pi(2 t-0.01 x) \,\,\,...(2)$
Comparing Eqs. (1) and (2), we get
$\frac{2}{\lambda}=0.01 $
$\Rightarrow \lambda=\frac{2}{0.01}=200\, m$