4.4 Waves, Fluids & Pressure

Why Waves and Fluids Matter

Wave behavior and fluid mechanics round out the NAPT physics content, and both connect directly to the Navy's operating environment: sonar and underwater acoustics rely on sound wave properties, while ship stability, submarine buoyancy control, and hydraulic systems throughout every vessel (steering gear, aircraft catapults, weapons elevators) rely on fluid pressure principles. This section covers standard wave and fluid physics, which you will apply constantly whether or not a specific question ever mentions a ship.

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). This is exactly how a small hydraulic pump can move a heavy rudder or lift a weapons elevator.

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. This is exactly how a steel ship floats despite steel being roughly eight times denser than water — the hull's shape displaces enough water that the buoyant force equals the ship's entire weight. Submarines use the same principle actively: flooding ballast tanks with seawater increases the sub's weight to submerge, and blowing the tanks with compressed air expels the water to reduce weight and surface.