10.1 Waves & Sound

Wave Fundamentals

A wave is a disturbance that propagates through a medium (or through vacuum, for electromagnetic waves) and transfers energy from one point to another without any net transport of matter. For the PAF GD Pilot Initial Test, you must distinguish the two mechanical wave types and relate them to aviation-relevant phenomena.

Transverse vs Longitudinal Waves

• Transverse wave — particles of the medium vibrate perpendicular to the direction of wave propagation. Example: waves on a string, electromagnetic waves (light, radio).
• Longitudinal wave — particles vibrate parallel to the direction of propagation, producing alternating compressions (high pressure) and rarefactions (low pressure). Example: sound waves in air.

Sound waves are longitudinal (compressional) mechanical waves — they require a material medium and cannot travel through a vacuum. This is why radio (electromagnetic) communication works in space but voice communication does not.

The Wave Equation

The fundamental relationship between wave speed v, frequency f, and wavelength λ is:

v = f × λ

where v is in m/s, f in hertz (Hz), and λ in metres (m). Frequency is set by the source and does not change when a wave crosses into a new medium; speed and wavelength do change.

Speed of Sound in Air

At 20°C and 1 atm, the speed of sound in air is approximately 343 m/s (often rounded to 340 m/s). It rises with temperature by about 0.6 m/s per 1°C. At 0°C it is roughly 331 m/s.

Worked example 1. A tuning fork vibrates at 680 Hz in air at 20°C. Find its wavelength.

λ = v / f = 343 / 680 ≈ 0.505 m (about 50 cm).

Worked example 2. A pilot sees lightning and hears thunder 3.0 s later. How far away is the storm (assume 20°C)?

distance = v × t = 343 × 3.0 ≈ 1029 m (about 1 km).

Intensity and Loudness

Intensity is the power carried per unit area (W/m²). Loudness is the human perception of intensity, measured in decibels (dB) on a logarithmic scale. A 10 dB increase corresponds to a 10× rise in intensity. The threshold of hearing is 0 dB; prolonged exposure above ~85 dB damages hearing — relevant for jet-engine mechanics and pilots.

Doppler Effect

The Doppler effect is the apparent change in frequency heard when there is relative motion between source and observer.

• Source and observer approaching → perceived frequency increases (pitch rises).
• Source and observer separating → perceived frequency decreases (pitch falls).

This is why a passing jet's engine note drops in pitch as it flies by.

Echo and Sonar

An echo is a reflected sound wave heard after a delay of at least 0.1 s (so the reflecting surface must be at least ~17 m away in air at 20°C, since sound must travel there and back: 2d = v × t).

Sonar (Sound Navigation And Ranging) uses echo timing underwater to measure depth and detect objects. Because sound travels at about 1500 m/s in water (much faster than in air), sonar is far more effective in water than in air.

Aviation Link: Mach Number and Sonic Boom

The Mach number is the ratio of an aircraft's speed to the local speed of sound: Mach = v_aircraft / v_sound. At Mach 1 the aircraft equals the speed of sound; above Mach 1 it is supersonic.

A sonic boom is the shock wave produced when an object travels faster than sound — pressure waves pile up into a cone (the Mach cone). For PAF GD Pilot candidates this is high-yield: Pakistan's fleet includes supersonic fighters (e.g., JF-17, F-16) where Mach-number awareness is operationally critical.

Doppler Effect — Quantitative Worked Example

For a stationary observer and a source moving toward it at speed v_s, the perceived frequency is:

f' = f × (v / (v − v_s))

where v is the speed of sound and f is the emitted frequency.

Worked example 3. A jet engine emits a tone at 600 Hz while approaching at 68.6 m/s (Mach 0.2 in air at 20°C, v = 343 m/s). What frequency does a stationary observer hear?

f' = 600 × (343 / (343 − 68.6)) = 600 × (343 / 274.4) = 600 × 1.25 = 750 Hz (pitch rises).

Once the jet has passed and is receding, the sign flips: f' = 600 × (343 / (343 + 68.6)) = 600 × 0.833 ≈ 500 Hz. The drop from 750 Hz to 500 Hz on fly-by is the familiar "wee-oo" effect, and the same physics governs radar Doppler shift used by ATC to measure aircraft ground speed.

Sonar Worked Example

Worked example 4. A sonar pulse sent downward returns 0.40 s after emission. How deep is the seabed (v_seawater ≈ 1500 m/s)?

The pulse travels down and back: 2d = v × t → d = (1500 × 0.40)/2 = 300 m. Notice the factor of 2 — a favourite PAF trap is forgetting that the pulse must travel to the target AND back.

Common Traps

• Frequency is set by the source — it does NOT change when sound enters water or crosses any boundary; only speed and wavelength change.
• Mach number depends on the LOCAL speed of sound, which falls with altitude/temperature. An aircraft flying at a fixed true airspeed can be subsonic at sea level and supersonic at altitude where the air is colder.
• Echo vs reverberation — an echo is a distinct repeat; reverberation is many rapidly blended reflections (the >0.1 s rule separates them).
• Sonar factor of 2 — always divide v × t by 2 for a one-way depth/distance; the pulse returns, so the travel time covers both legs.

Wave Properties at a Glance