Question

In stationary wave the distance between two successive nodes or two successive antinodes is equal to:
A. ${\mathbf{\lambda }}$
B. $\dfrac{{\mathbf{\lambda }}}{{\mathbf{2}}}$
C. $\dfrac{{\mathbf{\lambda }}}{{\mathbf{3}}}$
D. $\dfrac{{\mathbf{\lambda }}}{{\mathbf{4}}}$

Answer 1

Nodes and antinodes are considered to form waves that are stationary. The distance between these two consecutive nodes in a specified stationary wave is half the wavelength. In truth, the approximate distance between such a node and the next immediate antinode is one-fourth of the wavelength given.

Stepwise solution:

One feature of every standing wave pattern is there are points that seem to be standing still in the stream. Sometimes defined as points with no displacement, these points are called nodes. Here are some other points that undergo vibrations in the medium between a high positive as well as a major negative displacement. These points are, in a way, the reverse of nodes, which is why they are named antinodes.

The distance between the two successive nodes or two successive antinodes in a specific stationary wave is half of wavelength.

Hence, option B is correct.

Additional information:
Standing wave: The standing wave pattern is indeed a phenomenon of interference. The effect of the ideally timed collision of two waves moving through the same medium is that it is created. In truth, a standing wave is not really a wave; instead, it is the pattern arising from the interaction inside the same medium of two waves of same frequency with distinct travel directions.

Note:
We recognize that crests and troughs form a transverse wave. We also realise that one wavelength (i.e. one $\lambda$) is the distance between the two distinct crests or troughs. We know that half of wavelength is the difference between a crest and a successive trough, i.e. $\dfrac{\lambda }{2}$ .
Hence, the gap between two consecutive antinodes is therefore $\dfrac{\lambda }{2}$ .