The expression $y = a\, sin\, bx\, sin\, \omega t$ represents a stationary wave. The distance between the consecutive nodes is equal to
AIIMS 2011, Medium
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$y=a \sin b x \sin \omega t$
on comparing with standard equation of stationary wave
$y=R \sin \frac{2 \pi \mathrm{x}}{\lambda} \cdot \sin \omega \mathrm{t},$ we get
$\frac{2 \pi \mathrm{x}}{\lambda}=\mathrm{bx}$
$\lambda=\frac{2 \pi}{b}$
The distance between constructive nodes
$=\frac{\lambda}{2}=\frac{2 \pi / \mathrm{b}}{2}=\frac{\pi}{\mathrm{b}}$
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