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?
Wavelength 2 m, frequency 10 Hz
Wavelength 1 m, frequency 20 Hz
Wavelength 4 m, frequency 10 Hz
Wavelength 4 m, frequency 20 Hz
Sunlight enters a raindrop and a rainbow appears. Which sequence of optical processes inside the droplet produces the separated colors?
Absorption then transmission
Refraction, dispersion, internal reflection, refraction again
Reflection only
Diffraction and polarization
Which statement correctly compares light and sound?
Both can travel through a vacuum
Both are transverse waves
Sound travels faster in a vacuum than in air
Light slows down in water; sound speeds up in water
Sections you finish are checked off in the contents.