Physics (9702) | Transverse and longitudinal waves

Hello Future Physicist! Understanding Waves in Motion

Welcome to the fascinating world of waves! In the previous section (7.1), we learned that waves are all about transferring energy without transferring matter. But not all waves look or act the same.

This section is crucial because it teaches you how to classify the different types of progressive waves based on how the medium’s particles move. Mastering the difference between Transverse and Longitudinal waves is fundamental for the rest of your studies in oscillations and wave phenomena. Don't worry if the distinction seems tricky at first—we have great analogies to help!

7.2 Transverse and Longitudinal Waves

We classify waves based on the relationship between two directions:

1. The direction the energy (wave) is travelling (propagation direction).
2. The direction the particles of the medium vibrate (oscillation direction).

Let’s explore the two main types!

1. Transverse Waves

A transverse wave is a wave in which the direction of oscillation of the particles in the medium is perpendicular (at 90°) to the direction of energy transfer (propagation).

Key Characteristics of Transverse Waves

• Oscillation Direction: Perpendicular to propagation.
  Analogy: Imagine holding a rope and shaking it up and down. The pulse travels horizontally toward your friend, but the rope itself only moves vertically.
• Features: Transverse waves have alternating high points called crests (or peaks) and low points called troughs.
• Examples:
  • All Electromagnetic (EM) waves (like light, radio waves, X-rays).
  • Water ripples (on the surface).
  • Waves moving along a stretched string or rope.

2. Longitudinal Waves

A longitudinal wave is a wave in which the direction of oscillation of the particles in the medium is parallel to the direction of energy transfer (propagation).

Key Characteristics of Longitudinal Waves

• Oscillation Direction: Parallel to propagation (in the same direction).
• Analogy: Imagine pushing and pulling a Slinky spring horizontally. The compression travels down the spring (horizontal), and the coils themselves also move back and forth horizontally.
• Features: Instead of peaks and troughs, longitudinal waves have regions of:
  • Compression: Areas where the medium's particles are bunched together (high pressure/density). This corresponds to the crest of a transverse wave.
  • Rarefaction: Areas where the medium's particles are spread apart (low pressure/density). This corresponds to the trough of a transverse wave.
• Examples:
  • Sound waves travelling through air, liquids, or solids.
  • Primary (P) waves generated by earthquakes.

3. Comparing Wave Types (Syllabus Requirement 7.2.1)

The core difference is summarized clearly below. This is frequently tested!

Did you know? Polarisation (which you cover later in 7.5) is proof that light is a transverse wave. Polarisation is only possible if the wave disturbance is perpendicular to the direction of motion.

4. Analysing Graphical Representations (Syllabus Requirement 7.2.2)

Whether a wave is transverse or longitudinal, we usually represent it using a graph of displacement against distance (or displacement against time).

Interpreting Graphs for Transverse Waves

For a transverse wave (like a wave on a string), the interpretation is straightforward:

If you plot Displacement (y) vs. Distance (x):

• The y-axis directly shows the vertical movement of the particles.
• The Amplitude is the maximum value on the y-axis.
• The Wavelength (\(\lambda\)) is the distance between two successive crests or troughs.

Interpreting Graphs for Longitudinal Waves: A Challenge!

This is where students often get confused. A graph representing a longitudinal wave looks identical to a transverse wave graph (a sine or cosine curve), but the meaning of the displacement axis is different.

When plotting a longitudinal wave (like sound), the graph still shows Displacement (y) vs. Distance (x):

• Displacement (y-axis): This represents the shift of a particle from its equilibrium position, moving horizontally (parallel to the direction of propagation). A positive displacement means the particle has moved forward (in the direction of propagation), and negative means it has moved backward.
• Zero Displacement: Points where the displacement is zero (y=0) actually correspond to the centre of the Compression or the centre of the Rarefaction.
• Maximum Displacement (Amplitude): The crest and trough of the graph (maximum positive or negative displacement) correspond to the points halfway between a compression and a rarefaction where the medium is moving fastest.

Step-by-Step Graphical Analysis (Longitudinal)

Consider a displacement-distance graph for a longitudinal sound wave:

1. Identify points where displacement (\(x\)) is zero. At these points, particles are momentarily at their rest position.
2. Look at the gradient (slope) at these zero points:
   • If the gradient is negative (particles immediately ahead are moving backward, particles immediately behind are moving forward), this is a point of Compression (high density).
   • If the gradient is positive (particles immediately ahead are moving forward, particles immediately behind are moving backward), this is a point of Rarefaction (low density).
3. The Wavelength (\(\lambda\)) is still the distance between two successive points of compression or two successive points of rarefaction.

Key Takeaways for Transverse and Longitudinal Waves

• Transverse: Oscillation is Perpendicular. Features are Crests/Troughs. Includes light/EM waves.
• Longitudinal: Oscillation is Parallel. Features are Compressions/Rarefactions. Includes sound waves.
• Graphs: Both wave types are represented by displacement graphs. For longitudinal waves, maximum compression occurs where the particle displacement is zero but the density/pressure is highest.