The displacement of a wave is given by \(y=0 \cdot 002 \sin (100 t+x)\) where ' \(x\) 'and ' \(y\) ' are in metre and ' \(t\) ' is in second. This represents a wave

Comparing \(\mathrm{y}=0.002 \sin (\omega \mathrm{t}+\mathrm{x})\) with \(\mathrm{y}=\mathrm{a} \sin\) ( \(\omega \mathrm{t}+\mathrm{kx}\) )
We get \(\omega=100 \mathrm{rad} / \mathrm{s}\) and \(\mathrm{k}=1 \mathrm{rad} / \mathrm{m}\) and \(\mathrm{a}=0.002\)
\(\therefore \quad \mathrm{n}=\frac{\omega}{2 \pi}=\frac{100}{2 \pi}=\frac{50}{\pi} \mathrm{~Hz}\)
Velocity \(\mathrm{v}=\frac{\omega}{\mathrm{k}}=100 \mathrm{~m} / \mathrm{s}\) and \(\mathrm{k}=\frac{2 \pi}{\lambda}\)
\(\therefore \quad \lambda=\frac{2 \pi}{\mathrm{k}}=2 \pi \mathrm{~m}\)
Thus, it represents a wave travelling with a velocity of \(100 \mathrm{~m} / \mathrm{s}\) in the -ve direction.