Longitudinal and Transverse Waves — Revision Notes

⚡ 30-Second Revision

Wave: — Disturbance transferring energy, not matter.
Longitudinal Wave: — Particle oscillation parallel to wave propagation. Forms compressions & rarefactions. Examples: Sound waves, P-waves.
Transverse Wave: — Particle oscillation perpendicular to wave propagation. Forms crests & troughs. Examples: Light waves, waves on string, S-waves.
Wave Equation: — $v = flambda$ (Speed = Frequency $imes$ Wavelength).
Frequency ($f$): — Source-dependent, constant when changing medium.
Wavelength ($lambda$): — Distance between two consecutive similar points (e.g., crests).
Period ($T$): — $T = 1/f$.
Polarization: — Only possible for transverse waves (restricting oscillation plane).
Medium: — Longitudinal waves in all states of matter. Transverse waves in solids, surface of liquids, or no medium (EM waves).

2-Minute Revision

Waves are disturbances that transfer energy without transferring matter. They are categorized based on the direction of particle oscillation relative to wave propagation. Longitudinal waves have particles oscillating parallel to the wave's direction, creating regions of high density (compressions) and low density (rarefactions).

Sound waves are the primary example, capable of traveling through solids, liquids, and gases, and importantly, they cannot be polarized. Transverse waves, in contrast, have particles oscillating perpendicular to the wave's direction, forming crests and troughs.

Examples include light waves (electromagnetic waves), waves on a stretched string, and surface water waves. Transverse waves can be polarized, meaning their oscillations can be restricted to a single plane.

They generally require a medium with shear rigidity (like solids) or no medium at all (for electromagnetic waves). The fundamental wave equation, $v = flambda$, relates wave speed ($v$), frequency ($f$), and wavelength ($lambda$).

Remember that frequency is determined by the source and remains constant when a wave changes medium, while speed and wavelength change.

5-Minute Revision

Let's consolidate our understanding of longitudinal and transverse waves, crucial for NEET. A wave is essentially an energy transfer mechanism without net matter transport. The medium's particles oscillate around their equilibrium positions, passing energy to their neighbors.

Longitudinal Waves: Imagine a Slinky being pushed and pulled. The coils move back and forth along the Slinky's length, which is also the direction the wave travels. This 'back-and-forth' motion creates regions where particles are crowded (compressions) and regions where they are spread out (rarefactions).

Sound waves are the most common example. They can travel through solids, liquids, and gases because all these states of matter can be compressed and expanded. A key characteristic is that longitudinal waves cannot be polarized, as their oscillations are already confined to the single dimension of propagation.

Transverse Waves: Now, picture flicking a rope up and down. The rope moves vertically, but the wave travels horizontally. Here, particle oscillation is perpendicular to wave propagation. This creates distinct peaks (crests) and valleys (troughs).

Examples include light (all electromagnetic waves), waves on a stretched string, and surface water waves. Transverse waves typically require a medium with shear rigidity (like solids) to propagate through their bulk.

Importantly, transverse waves can be polarized, meaning their oscillations can be restricted to a specific plane perpendicular to the direction of travel.

Key Wave Parameters and Relations:

Wavelength ($lambda$): — Distance between two consecutive crests/troughs or compressions/rarefactions.
Frequency ($f$): — Number of oscillations per second. Determined by the source.
Period ($T$): — Time for one oscillation ($T = 1/f$).
Wave Speed ($v$): — Speed of energy propagation. Depends on the medium.
Wave Equation: — $v = flambda$.

Crucial Point for NEET: When a wave passes from one medium to another, its **frequency ($f$) remains constant**. Its speed ($v$) changes due to the new medium's properties, and consequently, its wavelength ($lambda$) also changes to satisfy $v = flambda$. For instance, if a sound wave goes from air to water, its speed increases, and thus its wavelength also increases, but its pitch (frequency) remains the same.

Example: A light wave has a frequency of $5 \times 10^{14},\text{Hz}$ in a vacuum. Its speed in a vacuum is $3 \times 10^8,\text{m/s}$. What is its wavelength? $lambda = v/f = (3 \times 10^8,\text{m/s}) / (5 \times 10^{14},\text{Hz}) = 0.6 \times 10^{-6},\text{m} = 600,\text{nm}$. If this light enters glass, its speed will decrease, and so will its wavelength, but its frequency will remain $5 \times 10^{14},\text{Hz}$.

Prelims Revision Notes

1
Wave Definition: — A disturbance that transfers energy without net transfer of matter. Particles oscillate around equilibrium.
2
Longitudinal Waves:

* Particle Motion: Parallel to wave propagation. * Wave Form: Compressions (high density/pressure) and Rarefactions (low density/pressure). * Medium: Can propagate through solids, liquids, and gases (requires elasticity for compression/expansion). * Polarization: Cannot be polarized. * Examples: Sound waves in any medium, P-waves (seismic primary waves), waves in a Slinky when pushed/pulled along its length.

1
Transverse Waves:

* Particle Motion: Perpendicular to wave propagation. * Wave Form: Crests (peaks) and Troughs (valleys). * Medium: Requires a medium with shear rigidity (solids, surface of liquids). Cannot propagate through the bulk of fluids (gases and liquids) due to lack of shear strength.

Electromagnetic waves (light) are transverse and do not require any medium. * Polarization: Can be polarized (oscillations restricted to a plane perpendicular to propagation). * Examples: Light waves (all electromagnetic spectrum), waves on a stretched string, S-waves (seismic secondary waves), surface water waves.

1
Key Wave Parameters:

* **Wavelength ($lambda$):** Distance between two consecutive points in the same phase (e.g., crest to crest). Unit: meter (m). * **Frequency ($f$):** Number of oscillations per second. Determined by the source.

Unit: Hertz (Hz or $s^{-1}$). **Crucially, $f$ remains constant when a wave changes medium.** * **Period ($T$):** Time for one complete oscillation. $T = 1/f$. Unit: second (s). * **Amplitude ($A$):** Maximum displacement from equilibrium.

Related to wave energy. * **Wave Speed ($v$):** Speed of energy propagation. Depends on the properties of the medium. Unit: m/s.

1
Wave Equation: — $v = flambda$.
2
Medium Change: — When a wave passes from one medium to another:

* **Frequency ($f$):** Remains constant. * **Speed ($v$):** Changes (depends on new medium's properties). * **Wavelength ($lambda$):** Changes (since $v$ changes and $f$ is constant, $lambda = v/f$ must change). * Amplitude: Usually changes due to reflection/absorption.

1
Sound vs. Light: — Sound is longitudinal, mechanical, needs medium, cannot be polarized. Light is transverse, electromagnetic, no medium needed, can be polarized.

Vyyuha Quick Recall

Longitudinal: Like Lining up, Like Sound. (Particles move along the line of wave travel, like sound waves.) Transverse: Turning To the side, To and fro. (Particles move perpendicular to wave travel, like light waves or a rope 'turning' up and down.)