Waves | Class 11 Physics Notes

14.2 Transverse and longitudinal waves

This section classifies mechanical waves based on the direction of oscillation of the medium's particles relative to the direction of wave propagation. If the particles oscillate perpendicular to the wave's direction, the wave is transverse; if they oscillate parallel, it is longitudinal.

For transverse waves, an example is a pulse traveling along a stretched string. When the string is given an up-and-down jerk, the disturbance moves along the string in the x-direction, while the string elements oscillate in the y-direction, perpendicular to propagation. If the jerk is continuous and sinusoidal, the resulting wave is a sinusoidal transverse wave. The displacement of the string elements varies sinusoidally with time at a fixed position and sinusoidally with position at a fixed time.

Longitudinal waves are illustrated by sound waves in air. A piston moving back and forth in a pipe compresses and rarefies air particles along the direction of wave propagation. This creates regions of higher and lower density that travel through the air. The oscillations of air particles are parallel to the wave direction.

The section emphasizes that in both wave types, the medium as a whole does not move with the wave; only the disturbance travels. For example, water waves involve particle motion that is both up and down and back and forth, combining transverse and longitudinal components.

Transverse waves require a medium that can sustain shear stress, such as solids, and therefore do not propagate in fluids. Longitudinal waves require only compressive elasticity and can propagate in solids, liquids, and gases. For example, steel can support both wave types, while air supports only longitudinal waves.

The section also introduces capillary and gravity waves on water surfaces, distinguished by wavelength and restoring forces (surface tension for capillary waves and gravity for gravity waves).

An example problem classifies various wave motions as transverse, longitudinal, or a combination, reinforcing the conceptual understanding.

📊 Diagram: Fig. 14.2 shows a pulse traveling along a stretched string in the x-direction with string elements oscillating up and down (y-direction). Fig. 14.3 shows a sinusoidal transverse wave on a string with elements oscillating perpendicular to wave direction. Fig. 14.4 shows longitudinal waves in air inside a pipe generated by piston motion, with air particles oscillating along the pipe (wave) direction.

🧪 Activity: Classify given wave motions as transverse, longitudinal, or combination based on particle displacement direction.

🔗 Connection: Prepares for the mathematical description of wave displacement relations in progressive waves in the next section.