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Resonance and damping IB DP Physics Study Notes

Waves extension IB DP Physics Study Notes - 2025 Syllabus

Resonance and damping IB DP Physics Study Notes

Resonance and damping IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • the nature of resonance including natural frequency and amplitude of oscillation based on driving
    frequency

  •  the effect of damping on the maximum amplitude and resonant frequency of oscillation

  •  the effects of light, critical and heavy damping on the system.

Standard level and higher level: 4 hours
Additional higher level: There is no additional higher level content .

IB DP Physics 2025 -Study Notes -All Topics

Damping

  • When some of the energy is removed from a standing wave, the result will be a decrease in the amplitude of the oscillations.
  • With light damping, the frequency of the oscillations remains relatively unchanged even as amplitude dececeases with time.
  • While light damping has minimal     impact on frequency, if the oscillator has heavy damping, the oscillator will move more slowly, extending the period of oscillation and returning to the equilibrium position more quickly.
  • If an oscillator is critically damped, it will quickly  return to the equilibrium position without ever passing it. This is useful in situation where   oscillations would normally occur, but we don’t  want them to, such as in shock absorbers.

Example:

A pendulum oscillates in air with gradually decreasing amplitude. Initially, its amplitude is \( 8.0 \, \text{cm} \), and after 5 complete oscillations, its amplitude drops to \( 4.0 \, \text{cm} \).

Assume damping is light and exponential. Estimate the damping coefficient \( b \), given that the time for 5 oscillations is 10 seconds.

▶️ Answer/Explanation

Amplitude decay equation:

\( A(t) = A_0 e^{-bt} \)

Substitute known values:

\( 4.0 = 8.0 \cdot e^{-b \cdot 10} \Rightarrow \frac{1}{2} = e^{-10b} \)

Take natural logarithm: \( \ln{\left(\frac{1}{2}\right)} = -10b \Rightarrow -\ln{2} = -10b \)

\( b = \frac{\ln{2}}{10} \approx \boxed{0.069 \, \text{s}^{-1}} \)

 

Forced Oscillations

  • A forced oscillation is when an outside, periodic force acts on a system. The effect of this regularly applied force can be dramatically different.
  • If you push a swing it will move away and  back toward you with it’s natural period. If you then apply the force again at the end   of its cycle, you are creating a forced oscillation at the natural or resonant frequency of the swing. 
  • Now consider if you pushed the swing when it was ¾ of the way through its cycle. What would be the effect?
  • Forced oscillations at the resonant frequency of the oscillator can dramatically increase the   amplitude of the vibrations. This is how you can shatter a wine glass with sound!
  • Forced oscillations not at the resonant frequency of the oscillator will cause vibrations, but will have limited amplitude.
 
●Superstring theory uses 11-dimensional standing waves as its particle model.
●Particles are “grainy” at the quantum level.
●The “extra” spatial dimensions required by string theory are “curled” in upon themselves and only visible at very small dimensions.

Example:

A child on a swing is pushed periodically every 2.0 seconds. The natural period of the swing is also 2.0 seconds. Explain the resulting motion and identify what type of oscillation this is.

▶️ Answer/Explanation

Explanation:

Since the driving frequency (one push every 2.0 s) equals the natural frequency of the swing, the swing undergoes **resonance**.

The amplitude of oscillation increases over time until limited by damping (air resistance, friction at pivot, etc.).

This is a case of forced oscillation with resonance.

Final Answer: Large amplitude oscillations occur due to resonance.

IB Physics Resonance and damping Exam Style Worked Out Questions

Question

The air in a pipe, of length l and open at both ends, vibrates with a fundamental frequency f. What is the fundamental frequency of a pipe of length 1.5l and closed at one end?

A. \(\frac{f}{3}\)

B. \(\frac{2f}{3}\)

C. \(\frac{3f}{2}\)

D. 3f

Answer/Explanation

Markscheme

A

Examiners report

Around the same number of candidates opted for A, B and C. The better candidates clearly favored the correct response, A. A quick and simple sketch reveals the answer immediately – this should be the candidates’ natural reaction given a resonance problem of this nature.

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