MCQ
The expression $y = a\, sin\, bx\, sin\, \omega t$ represents a stationary wave. The distance between the consecutive nodes is equal to
  • $\pi /b$
  • B
    $2\pi /b$
  • C
    $\pi /2b$
  • D
    $1 /b$

Answer

Correct option: A.
$\pi /b$
a
$y=a \sin b x \sin \omega t$

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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