Progressive Waves: Longitudinal & Transverse

• Direction of Oscillation: In a longitudinal wave, the particles of the medium oscillate back and forth parallel to the direction of energy transfer.

• Structural Features: These waves are characterized by compressions (regions where particles are close together, resulting in high pressure) and rarefactions (regions where particles are spread apart, resulting in low pressure).

• Polarization: Longitudinal waves cannot be polarized because their oscillation is already restricted to the same axis as the wave's travel.

• Examples: Sound waves in air, ultrasound, and primary (P) seismic waves are classic examples of longitudinal waves.

• Displacement ($x$): The distance and direction of a particle from its equilibrium position at any given time.

• Amplitude ($A$): The maximum displacement of a particle from its equilibrium position; it is directly related to the energy carried by the wave.

• Wavelength ($\lambda$): The distance between two consecutive points that are in phase, such as from crest to crest or compression to compression.

• Frequency ($f$): The number of complete oscillations passing a fixed point per unit time, measured in Hertz ($Hz$).

• Period ($T$): The time taken for one complete cycle of the wave to pass a point, related to frequency by $T = \frac{1}{f}$.

• Wave Speed ($v$): The speed at which energy is transmitted through the medium, calculated using the fundamental wave equation:

The Wave Equation: $v = f \lambda$

• Graph Interpretation: Be careful when reading displacement-time vs. displacement-distance graphs. A displacement-time graph for a single point looks identical for both transverse and longitudinal waves; you must check the description of particle motion to distinguish them.

• Phase Identification: Points are 'in phase' if they are at the same stage of their cycle (e.g., both at a crest). The distance between any two adjacent points in phase is exactly one wavelength ($\lambda$).

• Units Check: Always ensure frequency is in $Hz$ and wavelength is in meters ($m$) before calculating wave speed in $ms^{-1}$. Common traps include giving frequency in $kHz$ or wavelength in $cm$.

• Polarization as a Test: If a question asks how to prove a wave is transverse, the answer is usually to demonstrate that it can be polarized.