Question

Two identical progressive waves moving in opposite directions superimpose to produce a stationary wave. The wavelength of each progressive wave is \( \lambda \). The wavelength of the stationary wave is

• A. \( \dfrac{\lambda}{4} \)
• B. \( \dfrac{\lambda}{2} \)
• C. \( \lambda \)
• D. \( 2\lambda \)

Hint:

Stationary waves have the same wavelength as the progressive waves forming them.

Answer 1

The Correct Option is C

Step 1: Formation of stationary waves.
A stationary wave is formed by the superposition of two identical progressive waves having the same amplitude, frequency, and wavelength but traveling in opposite directions.

Step 2: Wavelength relation.
The wavelength of the stationary wave is equal to the wavelength of the individual progressive waves.

Step 3: Interpretation of nodes and antinodes.
In a stationary wave, the distance between two consecutive nodes or antinodes is \( \frac{\lambda}{2} \), but the full wavelength remains \( \lambda \).

Step 4: Final conclusion.
Hence, the wavelength of the stationary wave is \( \lambda \).