4.4 Waves, Fluids & Pressure

Editorial Scope

Waves, pressure, hydraulics, and buoyancy are included as public introductory physics. Their presence in this guide is editorial; it does not establish a NAPT physics blueprint or claim that a worked example models a Navy system.

Wave Properties

A wave is a disturbance that transfers energy through a medium (or, in the case of electromagnetic waves, through a vacuum) without any net transfer of matter. Four properties describe any wave:

• Wavelength (λ) — the distance between two successive corresponding points on a wave, such as crest to crest, measured in meters
• Frequency (f) — the number of complete wave cycles passing a fixed point per second, measured in hertz (Hz)
• Period (T) — the time required for one complete cycle, related to frequency by T = 1/f
• Amplitude — the maximum displacement from the rest position, which determines the wave's energy or intensity (but not its speed)

These properties combine into the fundamental wave equation:

v = fλ

where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m).

Worked Example 1: A sound wave travels through air at 343 m/s (the approximate speed of sound at room temperature) with a frequency of 440 Hz (the musical note A). Find its wavelength.

λ = v/f = 343 m/s ÷ 440 Hz ≈ 0.78 m

Worked Example 2: A wave has a wavelength of 2 m and travels at 6 m/s. Find its frequency.

f = v/λ = 6 m/s ÷ 2 m = 3 Hz

Fluid Mechanics and Pressure

Pressure (P) is force distributed over an area: P = F/A, measured in pascals (Pa), where 1 Pa = 1 N/m².

Pascal's Principle states that pressure applied to an enclosed, incompressible fluid is transmitted equally, undiminished, to every point in the fluid and to the walls of its container. This principle is the operating basis of every hydraulic system.

Worked Example: A hydraulic lift has a small piston with an area of 0.001 m² and a large piston with an area of 0.05 m². An operator applies 50 N of force to the small piston. Find the pressure created and the force produced at the large piston.

P = F/A = 50 N ÷ 0.001 m² = 50,000 Pa (50 kPa)

Since pressure transmits equally through the enclosed fluid (Pascal's Principle):

F2 = P × A2 = 50,000 Pa × 0.05 m² = 2,500 N

This is the mechanical advantage of a hydraulic system: 50 N of input force produces 2,500 N of output force — a 50-times multiplication, exactly matching the ratio of the two piston areas (0.05 ÷ 0.001 = 50). As a hypothetical public-textbook illustration, the same idealized principle could represent a rudder actuator or weapons-elevator lift; this is not a description of any Navy system or operating procedure.

Buoyancy: Archimedes' Principle

Archimedes' Principle states that an object submerged, fully or partially, in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces:

F_buoyant = ρ × V × g

where ρ is the fluid's density (kg/m³), V is the volume of fluid displaced (m³), and g is gravitational acceleration (9.8 m/s²).

Worked Example: An object with a volume of 0.002 m³ is fully submerged in fresh water (density = 1,000 kg/m³). Find the buoyant force acting on it.

F_buoyant = ρVg = 1,000 kg/m³ × 0.002 m³ × 9.8 m/s² ≈ 19.6 N

Whether an object floats or sinks depends on comparing this buoyant force to the object's weight: if the maximum possible buoyant force (at full submersion) is greater than or equal to the object's weight, it floats; if the object's weight exceeds the maximum buoyant force, it sinks. As a hypothetical public-textbook illustration, a hollow steel vessel can float when its overall shape displaces enough water for buoyant force to balance its weight. A simplified submarine example can likewise use ballast-water intake and compressed-air displacement to illustrate changes in average density; this is conceptual physics, not an operating procedure or system description.