Question

The particle displacement (in $cm$) in a stationary wave is given by $y(x,t)=2\sin \left(0.1\pi x\right)\cos \left(100\pi t\right)$. The distance between a node and the next antinode is:

• A. $2.5cm$
• B. $10cm$
• C. $7.5cm$
• D. $5cm$

Answer 1

The correct option is D $5cm$

$y(x,t)=2\sin \left(0.1\pi x\right)\cos \left(100\pi t\right)$
Compare with standard equation of standing wave,
$y=2A\sin \left(kx\right)\cos \omega t$
$k=0.1\pi$
$\omega =100\pi$
$k=\frac{2\pi }{\lambda }$
$\Rightarrow 0.1\pi =\frac{2\pi }{\lambda }$
$\Rightarrow \lambda =20cm$
The distance between a node and the next antinode,
$\Rightarrow \frac{\lambda }{4}=\frac{20}{4}=5cm$

Final answer: (𝒄)