Memory tricks for waves and sound

Source moving toward you → crests bunch up → higher frequency → higher pitch. Moving away → crests spread out → lower pitch. Used in radar, ultrasound, and astronomy.

Transverse waves (light, water surface): particles move perpendicular to wave travel. Longitudinal waves (sound): particles compress and rarefy parallel to travel direction. Sound cannot travel through a vacuum — light can.

Every object has a natural resonant frequency. Drive it at that frequency → amplitude grows. Tacoma Narrows Bridge (1940) is the classic example, though engineers now attribute its collapse to aeroelastic flutter rather than simple resonance. Basis of MRI, musical instruments, and radio tuning.

A standing wave appears stationary but is really two waves traveling in opposite directions. Nodes: points of zero amplitude. Antinodes: points of maximum amplitude. String instruments and organ pipes use this principle.

Constructive interference: waves in phase, amplitudes add. Destructive interference: waves out of phase (180°), amplitudes subtract. Superposition principle: resultant wave = sum of individual waves. Beats: two slightly different frequencies → periodic loud/soft pattern = beat frequency = |f₁ - f₂|.

0 dB: threshold of hearing. 60 dB: normal conversation. 120 dB: threshold of pain. Every 10 dB increase represents a 10-fold increase in intensity. 20 dB increase = 10 × 10 = 100× more intense. Perceived loudness doubles roughly every 10 dB.

Frequency (Hz): number of complete cycles per second → determines pitch for sound, color for light. Amplitude: maximum displacement from equilibrium → determines loudness for sound, brightness for light. Speed: set by the medium — sound travels faster in solids than liquids than gases.

All EM waves: travel at c in vacuum, are transverse, require no medium. Radio waves: lowest frequency, longest wavelength. Gamma rays: highest frequency, most energy. In a medium (glass, water): speed slows, wavelength shortens, but frequency stays the same — this is why light bends at interfaces.

Diffraction is most pronounced when the wavelength is comparable to the opening or obstacle size. Sound diffracts easily around corners (long wavelengths). Light diffracts less visibly (very short wavelength). Single slit and double slit diffraction patterns are classic exam problems.

Open pipe (open both ends): resonates at L = nλ/2. Fundamental frequency f₁ = v/2L. Has all harmonics. Closed pipe (one closed end): resonates at L = nλ/4 (odd n only). Fundamental f₁ = v/4L. Has only odd harmonics (1st, 3rd, 5th...). Flutes are open pipes, clarinets are closed.

Transverse waves oscillate perpendicular to travel — can be restricted to one plane (polarized). Light can be polarized by filters, reflection, or scattering. Polaroid sunglasses reduce glare by blocking horizontally polarized reflected light. Longitudinal waves (sound) oscillate parallel to travel — cannot be polarized.

v = fλ where v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m). Speed of sound in air: ~343 m/s at 20°C (increases with temperature). Speed of light in vacuum: c = 3×10⁸ m/s. In a medium: v = c/n where n is the refractive index. When a wave crosses into a new medium: frequency stays constant, speed and wavelength both change. Period T = 1/f. Angular frequency ω = 2πf.

When two waves of slightly different frequencies overlap, they alternately reinforce and cancel: f_beat = |f₁ − f₂|. At the beat: the waves are in phase (loud). Between beats: they are out of phase (quiet). Used for tuning instruments — when beats disappear, the two sources are at the same frequency. Faster beats = greater frequency difference. Used in ultrasound imaging (beat frequency between transmitted and reflected waves gives velocity via Doppler).

Radio waves: longest wavelength, lowest frequency, lowest energy. Microwaves: used in communication and cooking (resonates water molecules). Infrared: heat radiation, TV remotes. Visible: 400–700 nm (violet to red). Ultraviolet: causes sunburn, kills bacteria. X-rays: penetrates soft tissue, ionizing. Gamma rays: shortest wavelength, highest energy, most penetrating — from nuclear decay. Energy E = hf = hc/λ. Ionizing radiation: UV, X-ray, gamma (enough energy to knock electrons off atoms).

Mach number M = v_source / v_sound. M < 1: subsonic. M = 1: transonic (sound barrier). M > 1: supersonic — source outruns wavefronts → Mach cone forms. Half-angle of cone: sin θ = v_sound / v_source = 1/M. Sonic boom: the shock wave passing over an observer — not a one-time event but a continuous cone. Cherenkov radiation: same concept for charged particles moving faster than light in a medium — produces blue glow in nuclear reactors.