Wave Notes

Waves

Definition of a Wave

• A wave is an oscillation or disturbance that transfers energy through matter or space.
• Medium: The substance through which a mechanical wave travels.
• Example: A stadium wave where fans stand and raise their hands. Although the wave appears to move horizontally, only vertical motion occurs as each person rises and sits down.

Mechanical vs. Electromagnetic Waves

• Mechanical Waves:
  • Require a medium to travel.
  • Examples: sound waves, ocean waves, seismic waves, slinky waves.
• Electromagnetic Waves:
  • Do not require a medium to travel; they can travel through space.
  • Examples are found on the electromagnetic spectrum, including:
    • High-energy waves: gamma rays, X-rays, ultraviolet light.
    • Visible light.
    • Low-energy waves: infrared, microwaves, radio waves.

Sound Waves

• Sound waves transfer energy through air in longitudinal or compression waves.
• Sound cannot travel in a vacuum.
• Vibrations of objects produce sound waves (e.g., voice, musical instruments).
• Amplitude: Corresponds to loudness (how loud or soft a sound is).
• Frequency: Determines the pitch of a sound (high or low).
• Speed of Sound:
  • Sound travels slower than light (approximately $300$ meters per second in air).
  • The speed of sound changes depending on the medium. It travels faster through solids because molecules are closer together.

Energy Transfer by Waves

• Waves transfer energy, not matter.
• Even in ocean waves, individual water molecules move in a circular motion over a small area without net movement.

Types of Waves Based on Particle Movement

• Transverse Waves:
  • Particles are disturbed perpendicular to the direction of the wave.
  • Examples: light waves, spring waves moving up and down, surface seismic waves.
• Longitudinal Waves (Compression Waves):
  • Particles are disturbed back and forth parallel to the direction of the wave.
  • Examples: sound waves, some ocean waves, spring waves moving back and forth.

Frequency and Speed of Light

• Frequency: The number of wavelengths that pass each second; a measure of energy.
• High-energy waves (e.g., X-rays, gamma rays) travel at the same speed as low-energy waves (e.g., radio waves, microwaves).
• All light waves travel at the same speed in a vacuum: $3 \times 10^8$ m/s (the speed of light).

Characteristics of Waves: Amplitude, Wavelength, and Frequency

• Crest: The highest point a wave reaches above equilibrium.
• Trough: The lowest point a wave reaches below equilibrium.
• Amplitude:
  • The vertical distance from the equilibrium point to the crest.
  • Equals half the vertical distance from crest to trough.
  • In sound waves, amplitude corresponds to loudness.
• Wavelength (λ):
  • The distance between consecutive crests or troughs.
  • Humans can hear sound waves with wavelengths between approximately $0.02$ m (high pitches) and $20$ m (low pitches).
  • Humans can see light waves with wavelengths between approximately $4 \times 10^{-7}$ m (blue light) to $7 \times 10^{-7}$ m (red light).
• Frequency (f):
  • The number of times a wave cycles per unit time (typically 1 second).
  • Measured in Hertz (Hz), where $1$ Hz equals one cycle per second (1/s or $s^{-1}$).
  • A frequency of $100$ Hz cycles $100$ times in one second.
  • Waves with higher frequencies have more energy.
• Period (T):
  • The reciprocal of frequency: $T = \frac{1}{f}$.
  • The time it takes for a wave to complete one cycle or to move one wavelength.
• Wave Speed (v):
  • Equals the product of its frequency and wavelength: $v = fλ$.
  • Amplitude does not affect speed or frequency.

Relationship Between Frequency and Wavelength

• Higher frequency means shorter wavelength, and lower frequency means longer wavelength.
• High-energy waves have shorter wavelengths than low-energy waves.

Medium and Temperature Affect the Speed of Sound

• The denser the material, the faster sound travels.
• Light can travel through empty space. The speed of light in a vacuum is $3.00 \times 10^8$ m/s, represented as c in Einstein’s equation: $E = mc^2$.
• Light travels more slowly in denser mediums.

Reflection

• Reflection occurs when a wave strikes a boundary between two media and bounces back into the original medium.
• Example: Seeing your image in a mirror or on the surface of a lake.
• The law of reflection states that the angle of incidence ($\theta<em>i$) equals the angle of reflection ($\theta</em>r$).
• $\theta<em>i = \theta</em>r$
• During reflection, a wave’s direction changes, but its speed does not.
• Light can be transmitted (through transparent objects), partially transmitted (through translucent objects), or not transmitted at all (through opaque objects).

Refraction

• Refraction occurs when a wave is transmitted through a boundary, passing from one medium to another.
• Waves change speed as they transmit from one medium to another, causing them to bend.
• Different wavelengths of sunlight refract at different angles when passing through a raindrop, creating a rainbow.
• Objects reflect the frequencies (colors) of light that they don't absorb.
  • Red paper absorbs all frequencies except red, which is reflected.
  • White objects reflect most light; black objects absorb most light.

Diffraction and Interference

• Diffraction: When waves pass through a narrow slit or around a barrier, they spread out radially.
• Superposition: Two waves can occupy the same space at the same time.
• Interference: The net effect of two or more superimposed waves.
  • Constructive Interference: When the displacement of two waves is in the same direction, their amplitudes add together.
  • Destructive Interference: When the displacement of two waves is in opposite directions, they cancel each other out.

Acoustical Engineering

• Acoustical engineers apply the physics of sound to minimize or maximize the behavior of sound waves.
• Examples include designing recording studios with specialized foam padding to absorb sound waves and prevent reverberation or positioning speakers in outdoor music pavilions to account for refraction and diffraction.

The Doppler Effect

• The apparent change in frequency of a wave moving relative to an observer.
• Observed when the source of a wave is moving and the observer is still, or vice versa.
• Example: A police siren has a higher pitch as it approaches and a lower pitch as it moves away.

Wave Power

• Harnessing the mechanical energy in ocean waves to produce electrical energy.
• Wave movement turns gears in a turbine to create electric power.

Resonance

• Resonance occurs when an object or system oscillates at a large amplitude only when it is oscillating at a certain frequency or frequencies (resonant frequencies).
• Example: A tuned guitar string produces a particular sound because it vibrates with a large amplitude at its resonant frequency.
• Musical instruments like trumpets, flutes, and pianos rely on resonance.
• Resonance can also affect buildings and bridges, where engineers must ensure structures don’t vibrate at resonant frequencies due to wind.
• All musical instruments create standing waves that give music a fuller sound. Overtones come from standing waves created by constructive interference between sound waves traveling in both directions along a string or a tube.

Practical Applications of Sound and Light Waves in Technology

• The invention of the transistor revolutionized communication devices.
• Wireless technology advanced communication.
• New products are continuously being developed to improve data storage and transmission.