Wave model practice questions.

Which of the following is an example of a longitudinal wave?

• Light travelling through a vacuum
• A sound wave travelling through air
• Ripples on the surface of water
• A pulse travelling along a stretched string

Answer: A sound wave travelling through air

In sound, air molecules oscillate parallel to the direction of energy transfer (compressions and rarefactions) — the defining property of a longitudinal wave. The other three are transverse.

A graph shows the displacement of one particle of a medium against time as a wave passes. Which quantity can be determined directly from this graph?

• The wavelength of the wave
• The speed of the wave
• The period of the wave
• Both the wavelength and the speed

Answer: The period of the wave

A displacement–time graph for a single particle shows period (and amplitude). Wavelength requires a displacement–distance graph, and speed requires both graphs (v = λ/T).

Which region of the electromagnetic spectrum has the longest wavelength?

• X-rays
• Ultraviolet
• Infrared
• Radio waves

Answer: Radio waves

Radio waves have wavelengths from metres to kilometres — the longest in the EM spectrum — and correspondingly the lowest frequencies.

Water wave crests pass a fixed post at a rate of 12 every 30 s. Adjacent crests are 2.5 m apart. Determine the speed of the waves.

• 0.40 m s⁻¹
• 1.0 m s⁻¹
• 2.5 m s⁻¹
• 6.3 m s⁻¹

Answer: 1.0 m s⁻¹

f = 12/30 = 0.40 Hz and λ = 2.5 m, so v = fλ = 0.40 × 2.5 = 1.0 m s⁻¹. Choosing 0.40 or 2.5 means stopping after finding only f or λ.

A transverse wave travels along a stretched string. Two points on the string are exactly half a wavelength apart. Which statement about these two points is correct?

• At every instant their displacements are identical, because they are one full cycle apart.
• One of them is always at rest while the other is moving with its maximum speed.
• Their displacements are equal in magnitude only at the instants when both are at a crest.
• At every instant their displacements are equal in magnitude but opposite in direction.

Answer: At every instant their displacements are equal in magnitude but opposite in direction.

Half a wavelength corresponds to a phase difference of π, so the two points are in antiphase: when one is at a crest the other is at a trough, and both pass through zero together. A separation of a whole wavelength would be needed for identical displacements.

Which is the best estimate of the wavelength of visible light?

• 5 × 10⁻¹² m
• 5 × 10⁻⁷ m
• 5 × 10⁻⁴ m
• 5 × 10⁻¹ m

Answer: 5 × 10⁻⁷ m

Visible light runs from roughly 400 nm to 700 nm, so about 5 × 10⁻⁷ m. Wavelengths near 10⁻¹² m belong to gamma rays, 10⁻⁴ m to the infrared and 10⁻¹ m to radio waves — knowing these anchors makes a diffraction or interference answer easy to sanity-check.