Question

The distance between a node and an anti-node is
A. $2\lambda$
B. $\lambda$
C. $\dfrac{\lambda }{2}$
D. $\dfrac{\lambda }{4}$

Answer 1

From definition we know that an antinode and a node is $\dfrac{1}{2}$the distance between $2$consecutive nodes. Then we solve it using the formula $\lambda = 2(2 \times$Distance between a node and an antinode$)$.

Complete step by step solution:
Here,
From the definition we know that,
The wavelength of a wave is defined as having twice the distance between two consecutive nodes and antinodes.
Now,
The distance between an antinode and a node is $\dfrac{1}{2}$ the distance between $2$ consecutive nodes.
Therefore,
$\lambda = 2(2 \times$ Distance between a node and an antinode$)$
Hence,
The required distance is $\dfrac{\lambda }{4}$

Note: From definition we know that an antinode is the place where the wave’s maximum amplitude is generated by positive interference of the incoming and reflected waves. A node, by comparison, is the position where destructive interference reduces the amplitude of the wave to zero.