Question

Particle displacements (in $\text{cm}$) in a standing wave are 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. $2.5\text{cm}$
• B. $5.0\text{cm}$
• C. $7.5\text{cm}$
• D. $10.0\text{cm}$

Answer 1

The correct option is B $5.0\text{cm}$

General expression for a transverse standing wave :
$y=A\sin \left(kx\right)\cos \left(\omega t\right)$
Comparing with given equation,
$kx=\frac{2\pi x}{\lambda }=0.1\pi x$
$\Rightarrow \lambda =20\text{cm}$

The distance between a node and the next antinode $=\frac{\lambda }{4}=\frac{20}{4}=5\text{cm}$.
Hence, the correct choice is (b).