Question

Which of the following statements is correct for stationary waves?
A. Nodes and antinodes are formed in case of stationary transverse wave only
B. In case of longitudinal stationary wave, compressions and rarefactions are obtained in place of nodes and antinodes respectively
C. Suppose two plane waves, one longitudinal and the other transverse having the same frequency and amplitude are travelling in a medium in opposite directions with the same speed, by superposition of these waves, stationary waves cannot be obtained.
D. None of the above

Answer 1

Hint: In the case, if a problem is based on stationary waves, we know that there are two kinds of waves – longitudinal and transverse with different aspects hence, analyse every option with the scientific approach and check which option seems to be more appropriate for the given situation. Then, present the answer with a proper explanation.

Complete step by step solution:
A standing wave is a combination of two waves flowing in opposite directions that have the same amplitude and frequency. Interference causes the phenomena; that is, when waves are overlaid, their energies are either added together or wiped out.

We know that the point at which the displacement of particles of medium is zero is called a node and the point at which the displacement of particles of medium is maximum is called an antinode. This means the nodes and antinodes will be present in any kind of way whether it is a stationary transverse wave or stationary longitudinal wave. Therefore, options (A) and (B) are incorrect.

Secondly, the fundamentals of stationary waves say:
- To obtain a stationary wave, two waves must have the same frequency and must be travelling in opposite directions.
- They must be of the same nature i.e., either two waves should be longitudinal or transverse.

Hence, the correct answer is option C.

Note: Always keep in mind that interference of waves results in the creation of a travelling wave when waves are going in the same direction. When waves move in opposing directions, interference results in an oscillating wave that is stuck in space.