State the characteristics of stationary waves.

Question

Accepted Answer

The characteristics of a stationary wave, established across sections 6.5.2-6.5.3, are: (1) it is produced by the superposition of two IDENTICAL waves (equal amplitude, equal frequency) of the same kind (transverse or longitudinal), travelling through the medium along the SAME path but in EXACTLY OPPOSITE directions; (2) if the two interfering waves are transverse (as on a string), the resultant is a transverse stationary wave, with fixed points called NODES (permanently at rest) and points of maximum amplitude called ANTINODES, and points in between vibrating with amplitudes ranging from 0 up to the antinode's maximum value A; (3) if the two interfering waves are longitudinal (as in a pipe), the resultant is a longitudinal stationary wave, with the same node/antinode structure but conventionally represented using the same loop diagram, even though actual particle motion there is along the pipe's length; (4) the distance between two consecutive nodes, and separately between two consecutive antinodes, is always $\lambda/2$ ; (5) nodes and antinodes occur alternately, so the distance between a node and its nearest antinode is $\lambda/4$ ; (6) the amplitude of vibration varies PERIODICALLY IN SPACE (from node to antinode and back), while every particle (except exactly at a node) shares the SAME frequency of oscillation in time; (7) although every particle away from a node genuinely possesses energy, there is NO NET propagation of that energy along the medium -- it stays localised where it is produced, and the wave's own net velocity is zero, which is exactly why it is called 'stationary'; and (8) all particles WITHIN one loop vibrate exactly in phase with each other (no progressive phase change within a loop, unlike a progressive wave), while particles in adjacent loops are exactly 180 degrees out of phase, alternating loop by loop along the pattern. [!ANSWER] See the full list of characteristics in the working.

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set ANNUAL1 markMCQ
$Q. A string of length 2 m is vibrating with 2 loops. The distance between its node and adjacent antinode is ______.$
(a) 0.5 m
(b) 1.0 m
(c) 1.5 m
(d) 2.0 m
›Reveal solutionSolution

Each loop of a stationary wave is half a wavelength long, and a node–antinode gap is a quarter wavelength.

A string of length $L = 2\text{ m}$ vibrating in 2 loops means each loop has length $L/2 = 1\text{ m}$ . Since each loop corresponds to half a wavelength ( $\lambda/2$ ),

$\dfrac{\lambda}{2} = 1\text{ m} \;\Rightarrow\; \lambda = 2\text{ m}$

The distance between a node and the adjacent antinode in a stationary wave is always $\lambda/4$ :

$d = \dfrac{\lambda}{4} = \dfrac{2}{4} = 0.5\text{ m}$

✓Final answer
$0.5 m.$
CBSE 2024Set ANNUAL1 markMCQ
$Q. Phase difference between a node and an adjacent antinode in a stationary wave is ______.$
(a) π/4 rad
(b) π/2 rad
(c) 3π/4 rad
(d) π rad
›Reveal solutionSolution

Spatial phase between a node and the neighbouring antinode in a stationary wave.

For a stationary wave $y = 2A\cos(kx)\sin(\omega t)$ , a node occurs where $kx=0$ and the adjacent antinode where $kx=\pi/2$ (i.e. a quarter-wavelength away, $x=\lambda/4$ ). The spatial phase difference between these two points is therefore $\pi/2$ radians.

✓Final answer
$\pi/2$
CBSE 2018Set ANNUAL1 markMCQ
$Q. In stationary wave, the distance between a node and its adjacent antinode is ____.$
(a) $\lambda$
(b) $\lambda/4$
(c) $\lambda/2$
(d) $2\lambda$
›Reveal solutionSolution

Adjacent nodes (or adjacent antinodes) are $\lambda/2$ apart; a node and its neighbouring antinode are half of that, $\lambda/4$ apart.

A stationary wave is described by $y = 2a\cos(kx)\sin(\omega t)$ , where $k = 2\pi/\lambda$ . Nodes occur where $\cos(kx)=0$ , i.e. at $x = \lambda/4, 3\lambda/4, 5\lambda/4,\dots$ , and antinodes occur where $|\cos(kx)|=1$ , i.e. at $x=0,\lambda/2,\lambda,\dots$ . The separation between any node and its immediately adjacent antinode is therefore $\lambda/4$ , while the separation between two successive nodes (or two successive antinodes) is $\lambda/2$ .

✓Final answer
$\lambda/4$

Q.State the characteristics of stationary waves.

Concept understanding — Properties of Stationary Waves

Q.State the characteristics of stationary waves.

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