Study Notes on Light and Sound Waves

Fundamentals of Waves

• Definition: A wave is a disturbance or vibration that transfers energy from one location to another without the permanent transfer of matter.
• Transverse Waves: The vibration is perpendicular to the direction of travel. Light is an example of a transverse wave.
• Longitudinal Waves: The vibration is parallel to the direction of travel. Sound in the air is a longitudinal wave.
• Medium: The substance through which a wave travels, such as Air, Water, Steel, or Glass. Mechanical waves require a medium, while electromagnetic waves do not.

Essential Wave Properties

• Amplitude: The maximum displacement from the rest position. It represents energy; higher amplitude translates to louder sound or brighter light.
• Wavelength ($\lambda$): The distance between two consecutive corresponding points (e.g., crest to crest or trough to trough), measured in meters ($m$).
• Frequency ($f$): The number of complete waves passing a point per second, measured in Hertz ($Hz$). Higher frequency results in a higher pitch for sound and different colors for light.
• Wave Speed: Determined by the wave type and the medium. The relationship is defined by the formula: $\text{wave speed} = f \times \lambda$.

Wave Behaviors and Interactions

• Reflection: The bouncing back of a wave from a surface. The Law of Reflection states: $\text{Angle of incidence} = \text{Angle of reflection}$.
• Refraction: The bending of a wave as it passes between media of different densities due to a change in speed.
• Diffraction: The bending or spreading of waves around obstacles or through small openings.
• Interference: Occurs when waves meet. Constructive interference increases amplitude, while destructive interference decreases or cancels amplitude.
• Doppler Effect: The apparent change in frequency due to relative motion between the source and the observer. Moving toward the observer increases frequency and decreases wavelength.

Mechanics and Perception of Sound

• Nature of Sound: Sound is a longitudinal mechanical wave created by vibrations. It travels faster in solids and slower in gases.
• Pitch and Volume: Pitch is the human perception of frequency, while loudness is the perception of intensity (energy per unit area).
• Human Voice: Produced by exhaled air vibrating vocal cords between $100$ and $1,000$ times per second.
• Auditory Ranges:
  • Infrasound: Frequencies below $20\,Hz$.
  • Ultrasound: Frequencies higher than $20,000\,Hz$.

Light and the Electromagnetic Spectrum

• Light Speed: Light travels in a straight line at approximately $300,000\,km/s$ in a vacuum.
• Electromagnetic Spectrum: The range of all EM frequencies. In order of increasing energy and decreasing wavelength:
  1. Radio waves: Wavelengths longer than $0.3\,m$.
  2. Microwaves: The shortest radio waves.
  3. Infrared rays: Wavelengths from $0.001\,m$ to $7\,nm$, used in remote controls.
  4. Visible Light: The part of the spectrum humans can see, identifiable as ROYGBIV (red, orange, yellow, green, blue, indigo, violet).
  5. Ultraviolet (UV) rays: Wavelengths between $10\,nm$ and $400\,nm$.
  6. X-rays: Wavelengths from $1$ to $10\,nm$; can penetrate soft tissue but not dense bone.
  7. Gamma rays: The highest energy and shortest wavelengths ($1\,nm$ or less).
• Light Intensity: Depends on the amplitude of the wave, the distance from the source, and the power (the rate at which energy is emitted).