Wave Properties — Practice · Grade 12 Science

Chapter: Waves, Sound & Optics

What this practice covers

By the end of Wave Properties you should be able to:

11 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: wave, transverse wave, longitudinal wave, amplitude, wavelength (λ), frequency (f), interference.

Problem 1

A wave has a frequency of 10 Hz and a wavelength of 3 m. Find its speed.
Answer and explanation

30 m/s

v = f × λ = 10 × 3 = 30 m/s.

Problem 2

A wave has a period of 0.004 s. Find its frequency.
Answer and explanation

250 Hz

f = 1 ÷ T = 1 ÷ 0.004 = 250 Hz.

Problem 3

A wave travels at 12 m/s with a frequency of 4 Hz. Find its wavelength.
Answer and explanation

3 m

λ = v ÷ f = 12 ÷ 4 = 3 m.

Problem 4

In a transverse wave, the particles of the medium vibrate…
  1. parallel to the wave's motion
  2. perpendicular to the wave's motion
  3. in the exact direction the wave travels
  4. only when the wave stops
Answer and explanation

perpendicular to the wave's motion

Transverse means the vibration is perpendicular (at right angles) to the direction the wave travels.

Problem 5

Two waves of equal amplitude meet exactly out of phase (a crest of one lines up with a trough of the other). What happens where they overlap?
  1. the frequency doubles
  2. the wavelength doubles
  3. they cancel to zero amplitude
  4. their amplitudes double
Answer and explanation

they cancel to zero amplitude

Equal waves exactly out of phase interfere destructively and cancel — this is destructive interference.

Problem 6

A sound wave travels through water at 1500 m/s with a frequency of 300 Hz. Find its wavelength.
Answer and explanation

5 m

λ = v ÷ f = 1500 ÷ 300 = 5 m.

Problem 7

For f=10 Hz and λ=3 m, find speed. Show the reasoning, not just the conclusion.
Hints

Check v=fλ independently.

Answer and explanation

v=30 m/s.

Problem 8

How can wave energy move without each medium particle traveling the full wave distance?
Hints

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

Answer and explanation

Particles oscillate locally while interactions pass the disturbance and energy onward.

Problem 9

Use v=fλ with the medium and mode statedUse v=fλ with the medium and mode statedMedium/modelFrequencyWavelengthSpeedSpecified wave5 Hz2 m10 m/sSame speed, higher f10 Hz1 m10 m/sv=fλ connects cycles, distance per cycle and time.
Calculated compatible wave quantities; the two table rows assume the same nondispersive speed.
Interpret the supplied visual. At speed 340 m/s, what wavelength corresponds to 680 Hz?
Answer and explanation

λ=v/f=0.50 m under the stated medium conditions.

Wave speed satisfies v=fλ for a steady periodic traveling wave. Frequency is cycles per second and wavelength is meters per cycle, so their product gives meters per second. In a nondispersive medium, changing source frequency changes wavelength while speed stays approximately fixed. In a dispersive medium, speed can depend on frequency, so “speed is always fixed” is too broad. Identify the medium, wave type and relevant approximation.

λ=v/f=0.50 m under the stated medium conditions.

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 10

A wave has period 0.020 s and wavelength 0.80 m. Find frequency and speed. If frequency doubles in the same nondispersive medium, find the new wavelength.
Answer and explanation

f=50 Hz and v=40 m/s. At100 Hz with the same 40 m/s speed, λ=0.40 m.

f=50 Hz and v=40 m/s.

At100 Hz with the same 40 m/s speed, λ=0.40 m.

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.

Problem 11

OpenSciEd graph A of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd’s source graph has source position in millimeters versus time in seconds; it is not a spatial traveling-wave snapshot. Sound-source vibration graph A · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read approximate equilibrium position, amplitude, period and frequency from Graph A. Explain why the graph does not directly give wavelength or propagation speed.
Answer and explanation

The equilibrium is about 20 mm and amplitude about 0.8 mm, measured from that mean rather than from zero. Roughly three cycles occupy 0.01 s, givingT≈0.0033 s andf≈300 Hz. These are approximate visual readings. Time at one source does not provide spatial wavelength or wave speed without additional information.

Read source labels, scope, axes and intentional omissions.

Use the complete local explanation to draw a justified mechanism or calculate a supported quantity.

State what is observed, what is assumed and what evidence remains needed.

Response criteria

  • Interpret the source labels, units and scope accurately.
  • Explain the relevant mechanism with a labeled model or supported calculation.
  • Identify a meaningful assumption, uncertainty or missing comparison.

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