8.1 Waves: Light and Sound
Key Takeaways
- All waves transport energy without transporting matter; the universal wave equation v = fλ links wave speed, frequency, and wavelength, and a change in medium changes speed and wavelength but not frequency
- Transverse waves (light, electromagnetic) oscillate perpendicular to the direction of travel, while longitudinal waves (sound) oscillate parallel to travel through compressions and rarefactions
- The electromagnetic spectrum is ordered by frequency/wavelength from radio (low f, long λ) to gamma (high f, short λ); visible light is a narrow band roughly 400-700 nm
- Light reflects, refracts, disperses, is absorbed, and is transmitted; a rainbow is dispersion of sunlight by water droplets, a camera focuses light with a converging lens onto a sensor, and the human eye uses a lens and retina to form an image
- Sound is a longitudinal mechanical wave that requires a medium and travels faster in solids than in liquids than in gases; pitch corresponds to frequency and loudness to amplitude, and the Doppler effect shifts frequency when source and observer move relative to each other
Quick Answer: A wave carries energy without carrying matter. Two equations dominate this section: v = fλ (the wave equation) and the recognition that frequency does not change when a wave enters a new medium — only speed and wavelength do. Know the electromagnetic spectrum order, the differences between light (transverse, no medium) and sound (longitudinal, needs a medium), and the classic optical phenomena (reflection, refraction, dispersion).
Wave Anatomy and the Wave Equation
A wave is a repeating disturbance that transfers energy. The key descriptors:
- Wavelength (λ) — distance between two consecutive crests or troughes, in meters.
- Frequency (f) — number of cycles per second, in hertz (Hz); 1 Hz = 1/s.
- Amplitude — maximum displacement from the rest position; for mechanical waves, larger amplitude means more energy (louder sound, bigger water wave).
- Period (T) — time for one cycle; T = 1/f.
Wave equation: v = f × λ. A wave with frequency 10 Hz and wavelength 2 m travels at v = 10 × 2 = 20 m/s. If this wave enters a new medium where its speed drops to 10 m/s, its wavelength becomes λ = v/f = 10/10 = 1 m — the frequency stays 10 Hz; only speed and wavelength change.
Transverse vs. Longitudinal Waves
| Feature | Transverse wave | Longitudinal wave |
|---|---|---|
| Particle motion | Perpendicular to wave direction | Parallel to wave direction (compressions and rarefactions) |
| Examples | Light and all electromagnetic waves; a shaken string; water surface waves | Sound; spring (slinky) compression pulses; P-waves in earthquakes |
| Needs a medium? | EM waves do NOT; mechanical transverse waves do | Yes — longitudinal waves are always mechanical |
The Electromagnetic Spectrum
All EM waves travel at the speed of light in a vacuum (c ≈ 3 × 10⁸ m/s) and are transverse. They differ only in frequency and wavelength:
| Band | Approximate wavelength | Approximate frequency | Everyday use |
|---|---|---|---|
| Radio | > 1 m | < 3 × 10⁸ Hz | Broadcast radio, TV, Wi-Fi lower bands |
| Microwave | 1 mm – 1 m | 3 × 10⁸ – 3 × 10¹¹ Hz | Microwave ovens, radar, GPS, satellite comm |
| Infrared (IR) | 700 nm – 1 mm | 3 × 10¹¹ – 4 × 10¹⁴ Hz | Remote controls, thermal imaging, heat lamps |
| Visible | ~400 – 700 nm | ~4 – 7 × 10¹⁴ Hz | The only band human eyes detect (red ~700 nm, violet ~400 nm) |
| Ultraviolet (UV) | 10 – 400 nm | 7 × 10¹⁴ – 3 × 10¹⁶ Hz | Sunburn, sterilization, fluorescence |
| X-ray | 0.01 – 10 nm | 3 × 10¹⁶ – 3 × 10¹⁹ Hz | Medical imaging, airport security, crystallography |
| Gamma | < 0.01 nm | > 3 × 10¹⁹ Hz | Cancer radiotherapy, sterilization, produced by radioactive decay and cosmic events |
Frequency increases left-to-right; wavelength and energy per photon increase right-to-left. UV, X-ray, and gamma photons carry enough energy to ionize atoms and damage cells, which is why overexposure is hazardous.
Properties of Light
- Reflection — light bounces off a surface; the angle of incidence equals the angle of reflection. Mirrors, still water, echo-location analog in optics.
- Refraction — light bends when it crosses a boundary between media of different optical density, because its speed changes. A straw in a glass of water appears bent.
- Dispersion — different wavelengths bend by different amounts, separating white light into its colors. A rainbow forms when sunlight enters a water droplet, refracts and disperses, reflects off the inside back of the drop, and refracts again on the way out — the droplet acts like a tiny prism.
- Absorption — certain wavelengths are absorbed by the material; a red shirt absorbs all colors except red, which it reflects.
- Transmission — light passes through; clear glass transmits visible light.
Optical Systems
| System | How it works | Key optics |
|---|---|---|
| Camera | A converging lens focuses an image onto a sensor (or film); the aperture controls brightness and the shutter controls exposure time | Converging lens; real, inverted, reduced image |
| Microscope | An objective lens creates a magnified real image, and the eyepiece further magnifies that image for the eye | Two converging lenses; total magnification = objective × eyepiece |
| Human eye | The cornea and lens focus light onto the retina; the iris adjusts aperture; the ciliary muscle changes lens shape to focus at different distances (accommodation) | Converging cornea + lens; real, inverted image on retina |
| Rainbow | Sunlight disperses inside spherical raindrops, reflects internally, exits separated by color | Dispersion + internal reflection |
Nearsightedness (myopia) is corrected with a diverging lens; farsightedness (hyperopia) with a converging lens.
Properties of Sound
Sound is a longitudinal mechanical wave: it requires a medium (no sound in a vacuum) and travels as compressions and rarefactions of particles. Speed depends on the medium's stiffness and density:
- Air (20 °C): ~343 m/s
- Water: ~1,480 m/s
- Steel: ~5,960 m/s
Sound travels faster in solids because particles are closer and transmit compressions more quickly. Pitch corresponds to frequency (high f = high pitch); loudness corresponds to amplitude (larger amplitude = louder, in decibels). The human ear detects roughly 20 Hz – 20,000 Hz.
The Doppler effect is the apparent change in frequency when source and observer move relative to each other: an approaching ambulance siren sounds higher-pitched, then drops as it passes and recedes. Resonance is the large-amplitude response when a periodic force matches an object's natural frequency (a singer shattering a wine glass is the classic example). Interference of two sound waves can produce beats (alternating loud/soft) or standing waves in a tube or string, the basis of musical instruments.
Light vs. Sound: Quick Comparison
| Property | Light | Sound |
|---|---|---|
| Wave type | Transverse (EM) | Longitudinal (mechanical) |
| Needs a medium? | No (travels through vacuum) | Yes |
| Speed in air | ~3 × 10⁸ m/s | ~343 m/s |
| Speed in water vs. air | Slower in water | Faster in water |
| Frequency maps to | Color | Pitch |
| Amplitude maps to | Brightness | Loudness |
A common TExES trap is to assume sound and light both travel faster in the same direction of medium change — they do not. Light slows in denser media; sound speeds up because it depends on particle coupling, not just density.
A wave has a frequency of 10 Hz and a wavelength of 2 m. The wave then enters a new medium where its speed doubles. What are the new wavelength and frequency?
Sunlight enters a raindrop and a rainbow appears. Which sequence of optical processes inside the droplet produces the separated colors?
Which statement correctly compares light and sound?