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Physics 2 Unit 6: Waves, sound and physical optics

Light and sound are waves that interfere and diffract, which explains double-slit patterns, thin-film colors and standing waves.

Covers: Wave properties, sound and the Doppler effect, superposition and standing waves, the electromagnetic spectrum, interference, double-slit and diffraction gratings, thin films, polarization

Study guide

A wave transfers energy without transferring matter. Transverse waves oscillate perpendicular to the direction of travel (light, waves on a string), and longitudinal waves oscillate parallel to it (sound). Wave speed equals frequency times wavelength: v = fλ. The speed depends on the medium; frequency is set by the source. Sound is a longitudinal pressure wave that needs a medium and travels faster in solids than in gases. Loudness depends on amplitude (intensity, measured in decibels) and pitch depends on frequency. The Doppler effect is the change in observed frequency when a source and observer move relative to each other: approaching raises the observed frequency, and moving apart lowers it.

When waves overlap, superposition adds their displacements. Constructive interference occurs when crests meet crests, and destructive interference occurs when crests meet troughs. Standing waves form when waves reflect and interfere, creating nodes (no motion) and antinodes (maximum motion). On a string fixed at both ends, λ = 2L/n. In a tube open at both ends, λ = 2L/n; in a tube closed at one end, only odd harmonics occur and λ = 4L/n (n odd). Electromagnetic waves, ordered by increasing frequency as radio, microwaves, infrared, visible, ultraviolet, X-rays and gamma rays, all travel at c = 3.0 × 10⁸ m/s in a vacuum.

Physical optics treats light as a wave. In Young's double-slit experiment, light through two slits creates bright fringes where the path difference is a whole number of wavelengths: d sin θ = mλ. Dark fringes occur at half-wavelength differences. A diffraction grating uses many slits and follows the same equation, producing sharper bright lines. Diffraction is the spreading of waves around obstacles or through openings, most noticeable when the opening is about the size of the wavelength. In thin films, like soap bubbles and oil slicks, light reflects from both surfaces and interferes; a reflection off a higher-index medium causes a half-wavelength phase shift. Polarization filters transverse waves to one plane of vibration, which proves light is a transverse wave.

When the screen distance L is much larger than the slit spacing d, sin θ ≈ tan θ = y/L. So the mth bright fringe lies at y ≈ mλL/d, and neighboring bright fringes are Δy = λL/d apart. Longer wavelengths (lower frequencies) give more widely spaced fringes. A pulse reflected from a fixed end comes back inverted, and a pulse reflected from a free end comes back upright. When a wave passes into a medium where it travels more slowly, part of it reflects inverted and part is transmitted with a shorter wavelength but the same frequency.

A wave's energy is carried by its amplitude, and intensity is proportional to amplitude squared. For a point source spreading in all directions, intensity falls with the square of the distance (I = P/(4πr²)).

Key ideas

• v = fλ; speed depends on the medium, frequency on the source.
• The Doppler effect raises frequency when source and observer approach.
• Standing waves have nodes and antinodes set by boundary conditions.
• Double-slit bright fringes: d sin θ = mλ.
• Polarization shows light is a transverse wave.

Formulas and rules

Common mistakes

• Thinking frequency changes when a wave enters a new medium; speed and wavelength do.
• Thinking sound can travel through a vacuum; it needs a medium.

Words to know

Wave

A disturbance that transfers energy.

Transverse wave

A wave oscillating perpendicular to its direction of travel.

Longitudinal wave

A wave oscillating parallel to its direction of travel.

Wavelength

The distance between consecutive crests.

Frequency

The number of oscillations per second.

Amplitude

The maximum displacement of a wave.

Doppler effect

A change in observed frequency due to relative motion.

Superposition

Overlapping waves add their displacements.

Constructive interference

Waves combining to increase amplitude.

Destructive interference

Waves combining to decrease amplitude.

Standing wave

A wave pattern with fixed nodes and antinodes.

Node

A point of zero displacement in a standing wave.

Antinode

A point of maximum displacement in a standing wave.

Harmonic

A standing-wave frequency that's a multiple of the fundamental.

Electromagnetic spectrum

The full range of electromagnetic waves.

Double-slit experiment

Young's demonstration of light interference.

Diffraction

Waves spreading around obstacles or through openings.

Diffraction grating

A surface with many slits that produces sharp interference lines.

Thin-film interference

Interference of light reflected from both surfaces of a thin layer.

Polarization

Restricting a transverse wave to one plane of vibration.

Sample practice questions

5 more questions like these, from level 1 to 5, are in the practice set.