Waves in Fluids (Fluids)

Generation and propagation of acoustic and gravity waves in compressible fluid media.

General idea of the topic

A fluid can transmit disturbances in the form of waves. At the surface of a liquid, gravity and surface tension restore the shape and produce surface waves; in the interior of a gas or liquid, compressibility produces longitudinal pressure waves, which are sound.

The topic describes those two kinds of waves, their propagation speeds and the way the particles move, and introduces sound as the fundamental case of a longitudinal wave in a fluid.

What you will truly understand

By the end you will be able to distinguish surface from longitudinal waves, compute the speed of sound in a fluid from the bulk modulus and the density and recognize why surface waves depend on depth.

You will also be able to relate frequency, wavelength and speed.

Recommended learning route

1. Surface Waves: waves at the interface between a liquid and air, with circular motion of the particles.
2. Longitudinal Waves: compression waves in the interior of a fluid, with vibration along the direction of propagation.
3. Introduction to Sound: speed of sound, intensity and audible frequencies.

Physical criterion you must acquire

The essential criterion is not to confuse the motion of the wave with that of the fluid: the wave advances, but each particle only oscillates about its position. The speed of sound is v = √(K/ρ), and in a gas it depends on temperature, not on pressure alone.

Connection with real problems

• waves and surf.
• acoustics and ultrasound.
• sonar and ultrasonography.
• noise and architecture.

Final goal of the topic

The final goal is to understand how disturbances propagate in a fluid and compute speeds and wavelengths in each case.