Chapter 12: Waves

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Chapter Overview & SLOs

What is a wave? A wave is a disturbance that transfers energy from one point to another without transferring matter. Waves cause particles to oscillate around an equilibrium position, passing momentum from one particle to the next.

Why can''t we hear sound in space? Sound is a mechanical wave that requires a physical medium to propagate. Space is a vacuum with no molecules to transmit vibrations, so sound cannot travel in space.

What are the key wave properties?

| Property | Symbol | Definition | Unit | |----------|--------|------------|------| | Frequency | f | Number of oscillations per second | Hertz (Hz) | | Wavelength | λ | Distance between two consecutive crests/troughs | meters (m) | | Amplitude | A | Maximum displacement from equilibrium | meters (m) | | Time Period | T | Time for one complete oscillation | seconds (s) | | Wave Speed | V | Speed at which wave travels | m/s |

What is the wave equation? The fundamental wave equation is V = fλ, where V is wave speed, f is frequency, and λ is wavelength. Also, f = 1/T (frequency is reciprocal of time period).

What is the difference between transverse and longitudinal waves?

| Feature | Transverse Waves | Longitudinal Waves | |---------|-----------------|-------------------| | Particle motion | Perpendicular to wave direction | Parallel to wave direction | | Examples | Light, water waves, waves on a string | Sound waves, seismic P-waves | | Can travel in vacuum? | Electromagnetic waves can | No (require medium) |

How do water waves behave in shallow vs deep water? As water waves enter shallow water from deep water, their speed and wavelength decrease, while their frequency and time period remain constant (as they are determined by the source).

Under what conditions does maximum diffraction occur? Maximum diffraction occurs when the size of the aperture or obstacle is approximately equal to the wavelength of the wave (Aperture Size ≈ λ).

How is energy related to amplitude? The energy carried by a wave is directly proportional to the square of its amplitude: E ∝ A². Doubling the amplitude increases energy by a factor of 4.

What are seismic waves? Seismic waves are waves generated by earthquakes. There are two main types:

• P-waves (Primary waves): Longitudinal waves that travel through both solids and liquids. They are faster.
• S-waves (Secondary waves): Transverse waves that travel only through solids. They are slower.
• The S-wave shadow zone confirms the existence of Earth''s liquid outer core because S-waves cannot travel through liquids.

These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

• How do we relate wave speed, frequency, and wavelength? The fundamental wave equation is $V = f\lambda$; if the time period ($T$) of a vibration decreases, the frequency ($f$) increases proportionally because $f = 1/T$.
• How do water waves behave when entering shallow regions? As water waves enter shallow water from deep water, their speed and wavelength decrease, while their frequency and time period remain constant as they are determined by the source.
• Under what conditions does maximum diffraction occur? Maximum diffraction happens when the size of the aperture or obstacle is approximately equal to the wavelength of the wave ($\text{Aperture Size} \approx \lambda$).
• What insights do seismic waves provide about Earth's structure? P-waves (Primary) travel through both solids and liquids, but S-waves (Secondary) only travel through solids; the S-wave shadow zone confirms the existence of Earth's liquid outer core.

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