Energy Transportation Through Waves

Definition of a Wave

A wave is a disturbance that travels through space or matter, transferring energy without transferring mass.

Key characteristics:

• Carries energy from source to destination
• Doesn't require medium (or does, depending on type)
• Travels at specific speeds
• Can be reflected, refracted, or absorbed

Types of Waves

1. Mechanical Waves (Require Medium)

Travel through matter:

• Sound waves (air, water, solids)
• Water waves (surface ripples)
• Seismic waves (through Earth)

2. Electromagnetic Waves (No Medium Required)

Travel through empty space and matter:

• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays

Properties of Waves

1. Wavelength (λ)

Distance between consecutive crests or troughs

• Symbol: λ (lambda)
• Units: meters (m)
• Longer wavelength = lower frequency

2. Frequency (f)

Number of wave cycles passing a point per second

• Symbol: f
• Units: Hertz (Hz) = 1 cycle/second
• Higher frequency = shorter wavelength

3. Period (T)

Time for one complete cycle

• Symbol: T
• Units: seconds (s)
• Relationship: T = 1/f

4. Amplitude (A)

Maximum displacement from equilibrium

• Symbol: A
• Units: varies (meters for displacement, pressure for sound, etc.)
• Larger amplitude = more energy

5. Wave Speed (v)

Speed at which wave travels Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• λ = wavelength (m)

> [Ejemplo: A wave with f = 2 Hz and λ = 3 m: > - v = 2 × 3 = 6 m/s]

Sound Waves

What is Sound?

Sound is a mechanical wave (requires medium) created by vibrating objects.

Travels through:

• Air: ~343 m/s (at room temperature)
• Water: ~1,480 m/s (faster than air)
• Steel: ~5,000 m/s (faster than water)

Sound Characteristics

Pitch

• Related to frequency
• High pitch = high frequency
• Low pitch = low frequency

Loudness (Intensity)

• Related to amplitude
• Loud sound = large amplitude
• Soft sound = small amplitude

Loudness Scale (Decibels)

Important: Every 10 dB increase = 10× increase in intensity

Speed of Sound

Speed depends on medium:

• Air (20°C): 343 m/s
• Water: 1,480 m/s
• Steel: 5,000 m/s

Temperature effect in air: Speed increases ~0.6 m/s per °C

Applications of Sound

Ultrasound (frequency > 20 kHz):

• Medical imaging (ultrasound scan)
• Echolocation (bats, dolphins)
• Industrial cleaning

Infrasound (frequency < 20 Hz):

• Elephant communication
• Seismic monitoring
• Structural vibrations

Light and Electromagnetic Waves

What is Light?

Light is an electromagnetic wave (doesn't require medium).

Travels at constant speed:

(in vacuum)

Slightly slower in matter (different for each material).

The Electromagnetic Spectrum

Arranged by frequency/wavelength:

Visible Light

Only 400-700 nm wavelengths visible to human eye:

Remember: ROY G BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet)

Speed of Light Relationship

Where c = 3 × 10⁸ m/s

> [Ejemplo: Red light λ = 700 nm: > - f = c/λ = (3 × 10⁸)/(700 × 10⁻⁹) = 4.3 × 10¹⁴ Hz]

Energy of Waves

Energy Depends On

1. Amplitude² (for mechanical waves)

- Larger amplitude = more energy - Energy ∝ A²

1. Frequency (for all waves)

- Higher frequency = more energy - For electromagnetic waves: E = hf - Where h = Planck's constant = 6.63 × 10⁻³⁴ J·s

Intensity

Intensity = power per unit area

Units: W/m² (Watts per square meter)

• Decreases with distance (inverse square law)
• Proportional to amplitude squared

Wave Behaviors

Reflection

Wave bounces off surface:

• Angle of incidence = Angle of reflection
• Used in: mirrors, radar, sonar

Refraction

Wave bends when entering different medium:

• Speed changes → wavelength changes
• Frequency stays the same
• Example: light bending through glass

Diffraction

Wave bends around obstacles:

• More noticeable for longer wavelengths
• Sound diffracts around corners (why you hear around walls)
• Light diffracts but less noticeably (short wavelength)

Interference

Two waves interact:

• Constructive: Waves align → increased amplitude
• Destructive: Waves oppose → decreased or zero amplitude

Real-World Applications

Communication

• Radio: Long wavelength (AM, FM)
• Microwave: Cell phones, WiFi
• Visible light: Fiber optics, lasers

Medical

• Ultrasound: Pregnancy imaging, therapy
• Infrared: Thermal imaging, heat therapy
• X-rays: Bone imaging, CT scans
• Visible light: Endoscopy, phototherapy

Energy

• Solar: Light → electrical energy (photovoltaic cells)
• Thermal: Infrared radiation carries heat energy
• Sound: Acoustic energy in music halls, noise control

Key Takeaways

1. Wave = disturbance carrying energy through space/matter
2. Wavelength (λ) and frequency (f) are inversely related
3. Wave speed: v = f × λ (c = 3 × 10⁸ m/s for light)
4. Sound: Mechanical wave, speed ~343 m/s in air
5. Light: Electromagnetic wave, visible 400-700 nm
6. Amplitude related to loudness/brightness/intensity
7. Frequency related to pitch/color
8. Energy ∝ amplitude² (mechanical) and ∝ frequency (electromagnetic)