Forced Oscillations And Resonance
When soldiers marching across a footbridge break step, the reason relates to which phenomenon that can build up dangerously large oscillation amplitudes?
Select the correct option:
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About This Question
- Subject
- physics
- Chapter
- oscillations and waves
- Topic
- forced oscillations and resonance
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Resonance between driving frequency and natural frequency
Resonance, discussed in NCERT Class 11, Chapter 14 (Oscillations), occurs in a forced oscillator when the frequency of the external driving force matches the natural frequency of the system, producing a very large amplitude response. If marching soldiers step in unison at a rate close to the bridge's natural frequency, the periodic driving force pumps energy into the structure each cycle, and the amplitude can grow until the bridge is damaged. Breaking step randomizes the driving so no single frequency dominates. The option about total internal reflection belongs to optics and reflection of waves, not bridge oscillation. The option of destructive interference of footfalls is wrong because the danger comes from constructive reinforcement, not cancellation. The option of Doppler shifting concerns changes in observed frequency due to relative motion, not amplitude build-up. A plausibility check: energy fed in at the natural frequency accumulates because the driving stays in phase with the motion, so resonance correctly explains the observed danger; the amplitude at resonance is limited only by damping.
This easy difficulty physics question is from the chapter oscillations and waves, covering the topic of forced oscillations and resonance. It appeared in the 2025 exam.
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