9.2 Sound: Speed, Intensity, Pitch, Quality & Doppler Effect

Sound: Speed, Intensity, Pitch, Quality & Doppler Effect

This section completes Appendix I 2.5 Wave Motion and Sound for B1/B2 level 2 (not required for Category A). You will connect production of sound to the longitudinal wave model, quote the order of magnitude of speed of sound in air, distinguish intensity, pitch, and quality (timbre), apply the Doppler effect qualitatively, and introduce Mach number for high-speed flight—where Module 2 physics meets aerodynamic compressibility.

Production of Sound

Sound is the sensation (and the physical wave) associated with longitudinal mechanical waves in a frequency range the human ear can detect—roughly 20 Hz to 20 kHz for a young healthy listener, with many adults less sensitive at the high end. Sources produce sound by vibration: a speaker cone, a turbine blade row, a loose panel, a hydraulic pump, or a human vocal cord moves, and that motion couples into the surrounding medium.

Requirements for audible sound propagation:

1. A vibrating source that can disturb the medium.
2. A material medium (air, metal, liquid). Sound cannot cross a vacuum; radio and light can.
3. For hearing, a receiver (ear or microphone) sensitive to pressure fluctuations.

In air, sound is longitudinal: alternating compressions and rarefactions. The same v = fλ relation from 9.1 applies. Infrasound (below ~20 Hz) and ultrasound (above ~20 kHz) are still mechanical longitudinal waves but outside normal hearing; ultrasound appears in some NDT and industrial tools, while low-frequency vibration and rumble matter for structural and cabin comfort issues.

Aircraft are rich sound sources: engines (jet, propeller, APU), aerodynamic flow noise, landing gear, cabin environmental systems, and maintenance tools. Understanding frequency versus intensity helps you interpret noise reports, hearing-protection rules, and why a high-pitched whistle can be annoying even when overall sound level is moderate.

Speed of Sound in Air

The speed of sound (often written a or c in aerodynamics) is the speed at which small pressure disturbances travel through the medium. For dry air treated as an ideal gas, theory gives:

a = √(γ R T)

where T is absolute temperature (kelvin), R is the specific gas constant for air, and γ (gamma) is the ratio of specific heats (≈ 1.4 for air). The critical exam takeaway is qualitative and order-of-magnitude:

• Speed of sound in air depends primarily on temperature (and to a lesser extent on composition/humidity), not on frequency or amplitude of the wave for ordinary sound levels.
• Near ISA sea-level conditions, air temperature is 15 °C (288.15 K). The speed of sound is approximately 340 m/s (more precisely about 340–341 m/s; many textbooks round to 340 m/s or 343 m/s at 20 °C).
• Colder air → lower speed of sound; warmer air → higher speed of sound. At altitude, lower temperature reduces local a even though density also falls; Mach number uses the local speed of sound in the ambient air the aircraft flies through.

Order of magnitude to lock in: ~10² m/s class, specifically ≈ 340 m/s in air around 15 °C. Sound in solids and liquids is typically much faster (thousands of m/s in metals) because of higher elastic stiffness relative to density—useful when thinking about structure-borne noise and vibration paths through airframe structure versus airborne cabin noise.

Example using v = fλ. At a = 340 m/s, a pure tone of f = 1000 Hz has wavelength λ = a/f = 0.34 m. A 100 Hz tone has λ = 3.4 m. Low-frequency sound has long wavelength and diffracts more readily around obstacles; high-frequency sound is more directional and more easily blocked by barriers—relevant to noise control layout.

Do not confuse speed of sound with wind speed or true airspeed. Wind can carry the medium and shift effective ground-relative travel of a sound packet, but the intrinsic acoustic speed relative to the air is still set by air properties. Aircraft true airspeed (TAS) is compared to local a when forming Mach number (below).

Intensity

Intensity of a sound wave is the average power transported by the wave per unit area perpendicular to the direction of travel. SI unit: watt per square metre (W/m²).

Intensity increases with the square of amplitude (and depends on medium properties and frequency in full wave theory). The ear responds over an enormous range of intensities; human perception is often discussed on a logarithmic scale (decibels, dB), but Module 2 expects the physical idea: larger amplitude → higher intensity → generally louder, other factors equal. Distance from a small source reduces intensity roughly as inverse square of distance in free field (energy spread over a larger sphere), which is why standing close to a running engine or APU is far more hazardous to hearing than standing well clear.

Intensity is not the same as pitch. A quiet high-frequency beep and a loud low-frequency rumble differ in both frequency content and intensity. Hearing conservation in the hangar is about limiting intensity and exposure time, not about eliminating all frequency content.

Pitch

Pitch is the perceptual attribute that lets us call a sound “high” or “low.” Physically, for pure tones, pitch is determined almost entirely by frequency: higher f → higher pitch. A doubling of frequency is one octave in music language.

• Blade-pass frequencies, gear mesh frequencies, and electrical hum (e.g. related to 50 Hz or 400 Hz aircraft power systems in some equipment) all imprint characteristic pitches.
• Changing engine RPM changes the frequencies of many tones; the same v = fλ link means wavelength in air changes when f changes at fixed sound speed.

Trap reminder: period T = 1/f. A tone with a short period has a high frequency and therefore a high pitch. Saying “high period means high pitch” is wrong.

Quality (Timbre)

Two sounds can share the same fundamental frequency (same pitch) and similar overall intensity yet sound different—a pure tone generator versus a turbine whistle versus a human voice saying “ah.” That difference is quality or timbre.

Physically, quality depends on the waveform: which harmonics (integer multiples of the fundamental) are present and with what amplitudes and phases. A pure sine wave has only one frequency. Complex machinery noise is a spectrum of frequencies. Filters, resonators (ducts, cavities), and structural modes colour the spectrum—linking back to standing waves and resonance in 9.1 and periodic-motion material.

For the exam: pitch ↔ frequency; loudness/intensity ↔ amplitude/energy flux; quality/timbre ↔ waveform / harmonic content. Keep the three attributes separate in multiple-choice wording.

Doppler Effect

The Doppler effect is the change in observed frequency (and therefore pitch) when there is relative motion along the line joining source and observer.

Qualitative rules (Module 2 level):

• If source and observer approach each other, observed frequency increases → higher pitch.
• If source and observer recede, observed frequency decreases → lower pitch.
• If there is no component of relative velocity along the line of sight, there is no first-order Doppler shift.

Classic illustration: a siren or racing aircraft sounds higher on approach and lower after passing. The source still emits at its true frequency; wavelength ahead of a moving source is shortened (higher f for a stationary observer), and behind it is lengthened. When the observer moves, relative speed toward the wavefronts changes how many crests are encountered per second.

Exact algebraic forms (different for moving source vs moving observer) are often beyond the depth of a short Module 2 item, but the direction of the shift and the link approach → higher pitch are standard. Doppler radar and some airspeed or weather concepts in wider aviation use the same physics; here the requirement is the acoustic/frequency idea.

Note: Doppler changes frequency/pitch. It is not the same as intensity change with distance, though both can occur as an aircraft flies past (you hear pitch drop and loudness fall after the pass).

Mach Number and High-Speed Flight

Mach number links wave physics to flight:

M = V / a

where V is true airspeed of the aircraft (or flow speed) and a is the local speed of sound in the surrounding air.

Because a falls with temperature, the same TAS gives a higher Mach number in colder air (typical at altitude). Critical Mach number and drag-rise behaviour matter for high-speed jets; shock waves form when local flow reaches and exceeds sonic conditions. A sonic boom is associated with shock systems of supersonic flight—an extreme manifestation of pressure waves that cannot “get out of the way” ahead of a supersonic body in the same way as subsonic pressure fields.

For Module 2 you are not expected to design supercritical wings, but you are expected to know that:

1. Sound travels at a finite speed (~340 m/s in sea-level ISA air).
2. Mach number compares aircraft speed to that local acoustic speed.
3. Compressibility and shock-related phenomena become important as M approaches and exceeds 1.

This closes the loop from mechanical waves → sound speed → flight regime language used every day on type courses for fast aircraft.

Putting It Together for the Exam

• Production: vibration + medium → longitudinal sound wave.
• Speed: ~340 m/s in air near 15 °C; rises with temperature; v = fλ still holds.
• Intensity: power per unit area (amplitude-related); protect hearing.
• Pitch: frequency; Quality: waveform/harmonics.
• Doppler: approach raises pitch; recession lowers pitch.
• Mach: M = V/a; gateway to high-speed flight and compressibility.

Combined with 9.1, you can define wave parameters, avoid the T = 1/f trap, classify sound as longitudinal, and connect acoustics to Mach number—the operational payoff of wave motion for the licensed aircraft engineer.