A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:
Correct answer: C. 40 cm
- A. 10 cm
- B. 30 cm
- C. 40 cm
- D. 120 cm
Explanation
The correct answer is 40 cm. For a string fixed at one end and free at the other, the second harmonic corresponds to one full wavelength fitting within the length of the string. Since the string is 30 cm long, the wavelength of the constituent traveling waves is 60 cm, which matches Option C. Other options either understate or overstate the wavelength based on incorrect assumptions about the harmonic pattern.
This question appeared on the ETEA MDCAT 2016 paper, which you can sit online with every answer explained.
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About Stationary Waves
Stationary waves form when two waves of the same frequency and amplitude travel in opposite directions and interfere. The topic covers nodes, antinodes, wavelength, phase, resonance, and the allowed frequencies on strings and in air columns. Unlike progressive waves, stationary waves do not transfer energy from one point to another.
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