Wave Motion and Sound Waves

• Wave motion is the transfer of energy through an elastic medium via periodic disturbance.
• Energy transmitted down a rope has the capacity to effect change at its terminus by applying force
• Neither the rope itself, nor water particles necessarily move in the direction of energy transmission.
• Transverse waves are waves that move up and down, these can be represented by the values of Sin θ between 0° and 360°

Transverse Wave Forms

• Energy can propagate through an elastic medium with density changes.
• Compression is at the region of maximum density.
• Rarefaction is at the region of minimum density
• Compression, or longitudinal waves, are a set of pulses through a medium and can be mapped as sinusoidal waves.
• Sound waves, being compression waves, use the mechanical action of molecules to transfer action through a medium and cannot travel through a vacuum.

Compression Sound Wave Details

• Compression sound waves demonstrated via a tuning fork include rarefaction, compression, and sine waves.
• Light waves are electromagnetic radiation detectable by the human eye.
• Electromagnetic Radiation (EMR) is energy propagated with periodic electric and magnetic field strength variations caused by accelerating charged particles.
• Light waves are not mechanical waves, yet display similar behaviors and can travel through a vacuum.

Properties of Waves

• Waves possess amplitude (m), wavelength (λ), frequency (f), and a period (T)
• Amplitude measures maximum displacement/distance moved on a wave from its zero reference/equilibrium position
• Wavelength (λ, lambda) denotes one oscillation's length, identified from crest to crest
• Frequency (f) counts the number of wavelengths occurring per second
• Period (T) equals the time for one cycle and is found by (T=1/f)
• Speed of energy propagation (V) is given by (V=λf)
• If successive sea waves measure 200m with 10s intervals, energy propagates at 20 m/s

Wave Behaviour

• Refraction occurs when waves change direction due to a speed change
• Reflection happens when the system hits a solid barrier
• Diffraction describes how waves "bend" around an edge, initiating a new wave system
• The nature of light waves has been show to reflect and refract

Principle of Superposition

• When waves converge, their effects are algebraically added
• Identical sine waves overlaid produce a wave of same frequency with doubled amplitude
• Sine waves overlaid exactly half a phase out of sync cancel each other, this is used in noise-cancelling technology
• In Young's double-slit experiment, light through slits in a screen diffracts at the edges
• Light patterns displayed constructively and destructively interfere with light waves.
• Bright bands appear as light waves line up. Dark bands show where waves are cancelling

Standing Waves

• Standing waves form when a wave interferes with its own reflection, such as in a secured medium like a guitar string.
• The resultant wave is the superposition of the individual waves.
• Nodes are points of minimum amplitude, while antinodes are points of maximum amplitude
• Nodes have zero amplitude if colliding waves have equal amplitude moving in opposite directions
• Standing waves form when a fundamental wave interferes with a harmonic wave, producing multiples of the fundamental frequency.
• Resonance can create standing waves in structures causing fatigue at the antinodes
• Aircraft components can be affected

Helicopter Example

• Aircraft design must account for resonant frequency to prevent vibration amplification, where high vibration can destroy components.
• A helicopter's tail boom might have a resonant frequency of 3 Hz, oscillating three times per second when struck.
• If that rate of oscillation were achieved, the boom would vibrate at a frequency that would be a harmonic of one cycle per second (60 cycles per minute)
• Avoiding resonant vibrations is also important when designing wings and stabilizers

Beats

• Volume fluctuations occur when tuning two guitar strings to vibrate at nearly identical frequencies producing the beat frequency.
• These waves interfere, ears perceive varying intensity: maximum when additive, minimum when cancelling.
• Wave superposition explains this phenomenon
• Pilots synchronize propellers by ear to eliminate beat frequency noise induced by various propeler speeds

Sound

• Sound waves, those pressure-based frequencies that brains interpret, are heard by humans in frequencies between 20 Hz and twenty 20,000 Hz
• Pitch directly correlates to frequency, discernible by human auditory perception
• Sound stems from vibrating bodies such as vocal cords or airplane propellers traveling through the air
• As a sound source vibrates, compression and rarefaction periodically modulate air density
• This propagates with sound speed

Sound Speed

• Sound speed in air varies with temperature
• Sound travels at 660 kt (knots) or 340 m/s or 1224 km/h under standard sea-level atmospheric condition Aircraft make air disturbances that act like sound waves at same speed, often too faint for human detection.
• The ear is very sensitive; it can detect air pressure variations as small as about 0.000000005 Ib/in.2.
• Sound travels faster in liquids and solids

Sound Properties

• Intensity, measured in Watts per square meter (intensity I) - is the sound wave's amplitude, it is expressed as relative level is intensity level (IL).
• The decibal (dB) is the intensity metric, after Alexander Graham Bell. It gauges sound strength relative to average hearing sensitivity.
• Intensity Level is calculated using: IL = 10 log (I/Io) decibels (dB)
• 'I' signifies sound intensity (Watts/m^2)
• 'Io' represents hearing threshold (10^-12 Watts/m^2)
• 120dB is considered the 'threshold of pain'; prolonged exposure to sound of this intensity risks ear damage.

Intensity example

• Engine noise measures 10^-5 W/M^2

Sound Quality

• Quality/timbe sound relies on present harmonics, multiples of the original frequency (fundamental).
• In the figure, 196 HZ is the fundamental frequency. Instrument sound varies depending on the influence of its own characteristic harmonics

Speed of Sound Details

• Sound waves, identified as longitudinal compression waves, move through elastic media such are air.
• Wave speed varies per medium
• Under normal conditions at sea level, sound speed reaches 660kt (~340 m/s or 1224 km/h)
• Aircraft cause disturbances during movement, though they tend to be have an intensity insufficient to be detected
• Sound waves are created at less than the speed of sound (subsonic), but when the speed of sound if broken (supersonic) a shock wave is created
• The sound barrier is the immense jump in air pressure during this process

Mach Number

• At high speeds, aerodynamic forces rely on the Mach number.
• Flight Mach number is Aircraft TAS/ local speed of sound
• Air's local speed relies on its elasticity and temperature
• Speed versus altitude graph
• For air, local sound speed: a= 39√T knots (T in Kelvin)

Example of a sound calculation

• At 50,000 ft, local speed is 574 knots. Aircraft TAS: 600 kt.
• Flight Mach number = 600/574 = 1.05
• At 10,000 ft, local speed is 639 kt. Aircraft TAS: 600 kt.
• Flight Mach Number = 600/639 = 0.94

Doppler Effect

• Stationary sound source emits consistent frequency waves; a stationary listener recognizes the same frequency, from any location.
• Listeners in front of a moving source perceive a higher pitch

Doppler Effect in Application

• Perceived pitch lowers as sources recede
• Called the Doppler Effect, it affects waves where energy shifts based on source and listener motion If velocities are identical, pitch is constant between the stationary and moving source.
• Changing sound as cars, motorcycles, or planes approach/recede comes from this effect
• Astronomers monitor shifts toward red (lower) frequency ends of galaxy light to track their recession.