Question

If the particle displacement in a standing wave is given by y=2 sin (0.1 $\pi x$) cos 100 $\pi t$ cm, the distance between a node and the next antinode will be

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

Answer 1

Answer: (B)

5 cm

The displacement in a standing wave is given by

$y=2sin\left(0.1\pi x\right).cos\left(100\pi t\right)$ cm . . . . .(1)

The distance between a node and next anti-node will be

$S=\frac{\lambda }{4}$. . . . . . .(2)

From equation (1),

$k=0.1\pi =\frac{2\pi }{\lambda }$

$\lambda =20cm$

Put in equation (2), we get

$S=\frac{20}{4}=5cm$

The correct option is B.