Free C.4 Standing waves & resonance questions for IB Physics (SL & HL), part of C Wave behaviour. Each question has the answer and the marking points an examiner would look for.
Generate a full C.4 Standing Waves & Resonance worksheet →All C Wave behaviour questionsA driven oscillating system is lightly damped. The damping is then increased. What happens to the amplitude of the resonance peak and the frequency at which it occurs?
| amplitude at resonance | resonant frequency | |
|---|---|---|
| A | decreases | decreases slightly |
| B | unchanged | decreases slightly |
| C | increases | increases slightly |
| D | decreases | increases a lot |
Answer: A
The tension in a stretched string is multiplied by 9. The speed of waves on the string is proportional to the square root of the tension.
What happens to the fundamental frequency?
Answer: B
A pipe of length 0.85 m is closed at one end. The speed of sound is 340 m s−1.
Calculate the fundamental frequency.
Calculate the frequencies of the next two harmonics.
The pipe is opened at both ends. Calculate the new fundamental frequency.
Explain how a standing wave forms in the pipe.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 100 Hz λ = 4L = 3.4 m ✓ f = 100 Hz ✓ | 2 |
| (b) | 300 Hz and 500 Hz only odd harmonics ✓ 300 Hz and 500 Hz ✓ | 2 |
| (c) | 200 Hz λ = 2L = 1.7 m ✓ f = 200 Hz ✓ | 2 |
| (d) | superposition of reflected waves waves reflect at the end of the pipe ✓ two waves of the same frequency travelling in opposite directions superpose ✓ | 2 |
A tuning fork of frequency 512 Hz is held above a tube that is open at the top and closed at the bottom by water. The water level is lowered until the first loud sound is heard, at an air column length of 15.8 cm. The next loud sound is heard at 48.6 cm.
Explain how a standing wave is formed in the air column.
Sketch the standing wave patterns for the two lengths, labelling nodes and antinodes.
Use both lengths to determine the speed of sound.
Explain why using the difference in lengths gives a more accurate value than using the first length alone, and determine the end correction.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | reflection and superposition the sound wave reflects at the water surface ✓ the incident and reflected waves superpose to form a standing wave ✓ | 2 |
| (b) | quarter and three-quarter wavelength first: node at water, antinode at top (λ/4) ✓ second: N–A–N–A pattern (3λ/4) ✓ | 2 |
| (c) | 336 m s−1 difference in lengths = λ/2 ✓ λ = 2 × 32.8 cm = 0.656 m ✓ v = fλ = 336 m s−1 ✓ | 3 |
| (d) | 0.60 cm the antinode is slightly above the open end (end correction) ✓ this cancels when the difference is taken ✓ end correction = λ/4 − L1 = (L2 − 3L1)/2 = 0.60 cm ✓ | 3 |
A mass of 0.50 kg hangs on a spring of spring constant 200 N m−1. The top of the spring is driven up and down at different frequencies.
State what is meant by resonance.
Calculate the natural frequency of the system.
Describe the effect of increasing the damping on the amplitude–frequency graph.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | driving f = natural f, max amplitude maximum amplitude when the driving frequency equals the natural frequency ✓ | 1 |
| (b) | 3.2 Hz f = (1/2π)√(k/m) ✓ = 3.2 Hz ✓ | 2 |
| (c) | lower, broader peak peak amplitude is lower ✓ peak is broader and moves to a slightly lower frequency ✓ | 2 |
A guitar string 0.65 m long vibrates in its fundamental mode at 330 Hz.
Calculate the speed of waves on the string.
Calculate the frequency of the third harmonic.
Describe how the motion of two points either side of a node differs.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 429 m s−1 λ = 2L = 1.30 m ✓ v = 429 m s−1 ✓ | 2 |
| (b) | 990 Hz 990 Hz ✓ | 1 |
| (c) | antiphase they oscillate in antiphase (π out of phase) ✓ amplitudes depend on distance from node ✓ | 2 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in