Superposition, Standing Waves & Resonance — Practice · Grade 12 Science

Chapter: Waves, Sound & Optics

What this practice covers

By the end of Superposition, Standing Waves & Resonance you should be able to:

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: node, antinode, resonance.

Problem 1

Adjacent nodes are .30 m apart. Find wavelength.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

0.6 m

Node spacing=λ/2.

Problem 2

Does destructive interference permanently destroy waves?
Answer and explanation

No; it describes local combined displacement. The waves can continue and energy distribution must be considered.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

A fixed string has fundamental 15 Hz. Find fourth harmonic.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

60 Hz

4×15=60.

Problem 4

Why state boundary conditions?
Answer and explanation

Fixed, free, open, and closed boundaries allow different mode patterns.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

For the same string, find second-harmonic frequency. Show the reasoning, not just the conclusion.
Hints

Boundary conditions determine allowed wavelengths.

Answer and explanation

f₂=2f₁=20 Hz.

Problem 6

What happens when equal-amplitude waves meet exactly out of phase?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Their displacements cancel locally by superposition; this does not imply energy is destroyed everywhere.

Problem 7

Standing waves follow the allowed boundary patternStanding waves follow the allowed boundary patternnodenodenodeFixed ends: L=nλ/2; here n=2.
Original two opposite-phase snapshots of the same second-harmonic standing wave, not two traveling trajectories.
Interpret the supplied visual. For L=1.2 m in the shown second harmonic, what is λ?
Answer and explanation

L=2λ/2, so λ=1.2 m.

A standing wave has nodes of zero displacement amplitude and antinodes of maximum amplitude, produced by counterpropagating coherent waves under appropriate conditions. A string fixed at both ends has nodes there and supports L=nλ/2. The displayed second harmonic has an additional middle node. Air columns with an open end have different displacement/pressure boundary conditions; do not transfer the fixed-string formula without identifying what is constrained.

L=2λ/2, so λ=1.2 m.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

A 1.5 m string fixed at both ends has wave speed 30 m/s. Find its fundamental and third-harmonic frequencies and the third-harmonic wavelength.
Answer and explanation

f1=v/(2L)=10 Hz; f3=30 Hz. λ3=2L/3=1.0 m, with fixed-end nodes in this ideal string model.

f1=v/(2L)=10 Hz; f3=30 Hz. λ3=2L/3=1.0 m, with fixed-end nodes in this ideal string model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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