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Physics Unit 6: Oscillations and waves

Things that vibrate back and forth create waves, which carry energy without carrying matter.

Covers: Simple harmonic motion, springs and pendulums, wave properties, sound, interference and standing waves

Study guide

Simple harmonic motion (SHM) is periodic motion caused by a restoring force proportional to displacement, F = −kx. The object oscillates around equilibrium, moving fastest at equilibrium and stopping momentarily at the maximum displacement, called the amplitude. The period T is the time for one cycle, and frequency f = 1/T is cycles per second (hertz).

For a mass on a spring, T = 2π√(m/k): heavier masses oscillate more slowly and stiffer springs faster. For a simple pendulum with small swings, T = 2π√(L/g), which depends only on length and gravity, not on mass or amplitude. Energy in SHM trades between kinetic and potential energy.

A wave carries energy from place to place without carrying matter along. In transverse waves (like waves on a string or light), the medium vibrates perpendicular to the wave's direction; in longitudinal waves (like sound), it vibrates parallel, forming compressions and rarefactions. Wave properties include wavelength λ, frequency f, amplitude and speed, related by v = fλ. A wave's speed depends on the medium, not on its frequency.

Sound is a longitudinal mechanical wave that needs a medium; it travels about 340 m/s in air and faster in liquids and solids. Pitch depends on frequency and loudness on amplitude. The Doppler effect raises the observed frequency when the source and listener approach and lowers it when they separate.

When waves overlap, they combine by superposition. Constructive interference (crest meets crest) makes a bigger wave, and destructive interference (crest meets trough) cancels. Standing waves form when reflected waves interfere, with fixed nodes and maximum-motion antinodes; they create the specific harmonics of musical instruments.

Diffraction is the spreading of a wave as it passes through an opening or around an obstacle. It's strongest when the opening is about the size of the wavelength, which is why you can hear sound around a corner but can't see light around it. Every object has natural frequencies at which it vibrates most easily. If a periodic force or wave matches one of them, the amplitude grows larger and larger, which is called resonance. A tuning fork can start a matching fork vibrating, and soldiers break step on bridges to avoid it.

When a wave passes into a new medium, its frequency stays the same, set by the source. Its speed changes, so its wavelength changes in proportion (λ = v/f): a slower medium means a shorter wavelength. Light, radio waves, microwaves and X-rays are electromagnetic waves, transverse waves that need no medium and travel at 3.0 × 10⁸ m/s in a vacuum. Ordered from lowest to highest frequency (and energy), the spectrum runs radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Since T = 2π√(m/k), T² = (4π²/k)m. A graph of T² against m is a straight line with slope 4π²/k, so k = 4π²/slope. In the same way, a pendulum's T² plotted against L has slope 4π²/g.

Key ideas

• Springs: F = −kx pulls back toward equilibrium.
• Period depends on mass and spring constant (springs) or length (pendulums), not amplitude.
• Wave speed = frequency × wavelength.
• Transverse waves vibrate perpendicular to travel; sound is longitudinal.
• Interference: waves in phase add (constructive); out of phase cancel (destructive).

Formulas and rules

Common mistakes

• Thinking a bigger amplitude changes the period.
• Mixing up frequency (per second) with period (seconds per cycle).

Words to know

Wave speed

v = fλ

Period of a pendulum

2π√(L/g)

Frequency and period

f = 1/T

Longitudinal wave

Particles vibrate parallel to the wave's direction (like sound).

Constructive interference

Waves in phase add to a bigger amplitude.

Simple harmonic motion

Oscillation caused by a restoring force proportional to displacement.

Amplitude

Maximum displacement from equilibrium.

Period of a mass on a spring

T = 2π√(m/k)

Transverse wave

The medium vibrates perpendicular to the wave's direction.

Wavelength (λ)

The distance between matching points on consecutive waves.

Speed of sound in air

About 340 m/s.

Pitch / loudness

Set by frequency / set by amplitude.

Doppler effect

Observed frequency rises as source and listener approach.

Destructive interference

Crest meets trough and the waves cancel.

Standing wave

Interference producing fixed nodes and antinodes.

Superposition

Overlapping waves add together.

Sample practice questions

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