4.5 Waves, Sound & the Electromagnetic Spectrum

4.5 Waves, Sound & the Electromagnetic Spectrum

A wave is a repeating disturbance or oscillation that transfers energy from one location to another without transferring matter. When a wave passes through a medium (such as water or air), the medium's particles vibrate around a fixed position, but do not travel along with the wave.

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Classification of Waves

Physics categorizes waves based on two criteria: whether they require a physical medium and their direction of particle vibration.

1. Mechanical vs. Non-Mechanical Waves

• Mechanical Waves: Require a physical substance or medium (solid, liquid, or gas) to propagate. They cannot travel through a vacuum. Examples: Sound waves, water waves, seismic earthquake waves, slinky waves.
• Non-Mechanical (Electromagnetic) Waves: Do not require a physical medium. They propagate through electric and magnetic field oscillations and travel through empty vacuum space. Examples: Visible light, X-rays, radio signals, microwaves.

2. Transverse vs. Longitudinal Waves

Transverse Wave:    /\  Crest   /\
                  -/--\-------/--\---> Wave Direction
                       \/ Trough  \/

Longitudinal Wave: |||||  |  |  |  |||||  |  |  |  ||||| ===> Wave Direction
                   Compression   Rarefaction  Compression

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Key Wave Parameters & The Wave Equation

Every wave is defined by four core physical parameters:

1. Wavelength ($\lambda$, Lambda): The distance between two consecutive identical points on a wave (e.g., crest-to-crest or compression-to-compression), measured in meters ($\text{m}$).
2. Frequency ($f$): The number of complete wave cycles passing a fixed point per second, measured in Hertz ($\text{Hz} = 1/\text{s}$).
3. Period ($T$): The time required for one full wave cycle to pass ($T = \frac{1}{f}$), measured in seconds ($\text{s}$).
4. Amplitude ($A$): The height of a wave from equilibrium to crest. Amplitude measures the energy carried by the wave (e.g., larger sound amplitude = louder volume; larger light amplitude = brighter intensity).

The Universal Wave Equation

$\text{Wave Speed } (v) = \text{Frequency } (f) \cdot \text{Wavelength } (\lambda)$

• Inverse Relationship: For a wave traveling through a constant medium (where speed $v$ is fixed), frequency and wavelength are inversely proportional. High frequency means short wavelength; low frequency means long wavelength.

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Sound Waves

Sound is a mechanical, longitudinal wave produced by vibrating objects.

Characteristics of Sound Propagation:

• Requires a Medium: Sound cannot travel through outer space or a vacuum because there are no gas/liquid/solid molecules to transmit compressions.
• Speed Depends on Medium Elasticity and Density: Sound travels fastest in rigid solids, slower in liquids, and slowest in gases: $\text{Speed of Sound: } v_{\text{solid}} > v_{\text{liquid}} > v_{\text{gas}}$ (In dry air at $20^\circ\text{C}$, sound speed is $\approx 343\text{ m/s}$; in water, $\approx 1480\text{ m/s}$; in steel, $\approx 5960\text{ m/s}$).
• Pitch vs. Loudness:
  • Pitch is determined strictly by wave frequency (High frequency = High pitch treble; Low frequency = Low pitch bass).
  • Loudness is determined by wave amplitude and intensity, measured in decibels ($\text{dB}$).

The Doppler Effect

When a sound source moves relative to an observer, the observed frequency shifts:

• Approaching Source: Sound waves compress together $\implies$ higher frequency / higher pitch.
• Receding Source: Sound waves stretch apart $\implies$ lower frequency / lower pitch.
• Example: The pitch of an ambulance siren sounds high as it drives toward you and drops noticeably lower as it passes and moves away.

The Electromagnetic (EM) Spectrum

Electromagnetic waves are transverse non-mechanical waves traveling through vacuum space at the speed of light ($c \approx 3.0 \times 10^8\text{ m/s} = 300,000\text{ km/s}$).

The EM spectrum is a continuous range of electromagnetic radiation ordered by wavelength, frequency, and photon energy.

The Electromagnetic Spectrum Continuum

<-- Long Wavelength (Low f, Low Energy) ------- Short Wavelength (High f, High Energy) -->
Radio Waves | Microwaves | Infrared | Visible Light | Ultraviolet | X-Rays | Gamma Rays
                                       (ROYGBIV)

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Wave Behaviors & Interactions

When waves encounter obstacles or boundaries between different media, four primary interactions occur:

1. Reflection: A wave bounces back after striking a boundary (e.g., an echo for sound, a mirror image for light). Law of Reflection: Angle of Incidence = Angle of Reflection.
2. Refraction: The bending of a wave as it passes at an angle from one medium into another with a different wave speed (e.g., a straw appearing bent in a glass of water due to light slowing down in water relative to air).
3. Diffraction: The bending or spreading of waves as they pass through narrow openings or around obstacles (e.g., hearing sound from around a doorway corner).
4. Absorption & Transmission: When light strikes matter, energy is either absorbed (converted to heat) or transmitted through (passed through transparent materials).