🌀Principles of Physics III Unit 2 – Sound Waves

What's Sound, Anyway?

• Sound consists of vibrations that travel through a medium (solid, liquid, or gas) as a mechanical wave
• Vibrations cause particles in the medium to oscillate back and forth, creating areas of compression and rarefaction
• Human ears detect sound waves when vibrations reach the eardrum, causing it to oscillate
• Audible frequency range for humans spans from about 20 Hz to 20 kHz
  • Frequencies below 20 Hz are called infrasound (elephants, whales)
  • Frequencies above 20 kHz are called ultrasound (bats, dolphins)
• Sound waves require a medium to propagate and cannot travel through a vacuum
• Speed of sound varies depending on the medium (fastest in solids, slowest in gases)

Wave Basics: The Building Blocks

• Sound waves are longitudinal waves where particles oscillate parallel to the direction of wave propagation
• Key parameters of sound waves include wavelength, frequency, amplitude, and speed
  • Wavelength ($\lambda$) represents the distance between two consecutive compressions or rarefactions
  • Frequency ($f$) measures the number of wave cycles passing a fixed point per unit time (Hz)
  • Amplitude corresponds to the maximum displacement of particles from their equilibrium position
• The speed of sound ($v$) in a medium is determined by its properties, such as density and elasticity
• Relationship between speed, wavelength, and frequency is given by the equation: $v = \lambda f$
• Sound waves exhibit properties like reflection, refraction, diffraction, and interference
• Constructive interference occurs when waves are in phase, resulting in increased amplitude
• Destructive interference occurs when waves are out of phase, leading to decreased amplitude

Types of Sound Waves

• Sound waves can be categorized based on their frequency, wavelength, and source
• Pure tones consist of a single frequency and are rarely found in nature (tuning fork)
• Complex tones are made up of multiple frequencies and are more common in real-world sounds (musical instruments)
  • Fundamental frequency is the lowest frequency component of a complex tone
  • Harmonics are integer multiples of the fundamental frequency that contribute to the overall timbre
• Noise refers to irregular or random vibrations with no discernible pitch (white noise, pink noise)
• Infrasonic waves have frequencies below the human audible range (< 20 Hz) and can travel long distances
• Ultrasonic waves have frequencies above the human audible range (> 20 kHz) and are used in various applications (medical imaging, cleaning)

Properties of Sound

• Pitch is the perceived frequency of a sound, with higher frequencies corresponding to higher pitches
  • Pitch depends on the frequency of the sound wave and the listener's perception
  • Musical notes are assigned specific frequencies (A4 = 440 Hz)
• Loudness is the subjective perception of sound intensity, related to the amplitude of the wave
  • Sound intensity ($I$) is the power per unit area, measured in watts per square meter (W/m²)
  • Decibel scale (dB) is used to express sound intensity levels relative to a reference level
    • Threshold of human hearing is 0 dB (1 picowatt/m²)
    • Each 10 dB increase represents a tenfold increase in sound intensity
• Timbre is the characteristic quality of a sound that distinguishes it from others with the same pitch and loudness
  • Timbre is determined by the relative amplitudes and phases of the harmonics in a complex tone
  • Allows us to differentiate between different musical instruments or voices

How Sound Travels

• Sound waves propagate through a medium by transferring energy from one particle to another
• In gases, sound travels as longitudinal waves, with particles oscillating in the direction of wave propagation
  • Compressions are regions of high pressure and particle density
  • Rarefactions are regions of low pressure and particle density
• Speed of sound in gases depends on factors like temperature, humidity, and atmospheric pressure
  • At standard temperature and pressure (20°C, 1 atm), the speed of sound in air is approximately 343 m/s
• In liquids and solids, sound can also travel as transverse waves, with particles oscillating perpendicular to the direction of wave propagation
  • Speed of sound is generally higher in liquids and solids compared to gases due to closer particle spacing and stronger intermolecular forces
• Sound waves can be reflected, refracted, or diffracted when encountering boundaries between different media
  • Reflection occurs when sound waves bounce off a surface (echo)
  • Refraction occurs when sound waves change direction due to a change in the medium's properties (underwater acoustics)
  • Diffraction occurs when sound waves bend around obstacles or through openings (sound heard around corners)

Measuring and Analyzing Sound

• Microphones are devices that convert sound waves into electrical signals for recording or analysis
  • Different types of microphones (dynamic, condenser, ribbon) have varying sensitivity and frequency response
• Oscilloscopes and spectrum analyzers are used to visualize and measure sound wave properties
  • Oscilloscopes display the waveform of a sound signal in the time domain (amplitude vs. time)
  • Spectrum analyzers display the frequency content of a sound signal in the frequency domain (amplitude vs. frequency)
• Fourier analysis is a mathematical technique used to decompose complex sounds into their constituent frequencies
  • Fourier transform converts a time-domain signal into its frequency-domain representation
  • Allows for the identification of individual frequency components and their relative amplitudes
• Sound level meters are used to measure sound pressure levels in decibels (dB) for various applications (noise pollution, hearing protection)
• Acoustic impedance is a measure of a medium's resistance to the flow of sound energy
  • Impedance matching is important for efficient energy transfer between different media (speaker design, ultrasound imaging)

Real-World Applications

• Acoustic engineering involves the design and optimization of spaces and devices for desired sound characteristics
  • Concert halls and recording studios are designed to provide optimal acoustics and minimize unwanted reflections
  • Noise reduction and sound insulation techniques are used in buildings, vehicles, and industrial settings
• Ultrasound imaging uses high-frequency sound waves to create images of internal body structures
  • Commonly used in medical diagnostics (pregnancy, cardiovascular imaging) and non-destructive testing
• Sonar (Sound Navigation and Ranging) uses sound waves to detect and locate objects underwater
  • Used in marine navigation, fishing, and underwater exploration
• Seismology utilizes sound waves (seismic waves) to study the Earth's interior and monitor earthquakes
  • P-waves (primary waves) and S-waves (secondary waves) provide information about the Earth's structure and composition
• Music and speech synthesis rely on the manipulation of sound waves to create desired sounds
  • Synthesizers generate and combine various waveforms to produce musical sounds
  • Speech synthesis algorithms convert text into artificial speech by modeling the human vocal tract

Cool Sound Phenomena

• Doppler effect is the apparent change in frequency of a sound wave as the source and observer move relative to each other
  • Observed in everyday life (ambulance siren, passing train)
  • Used in radar and medical imaging to measure velocities
• Sonic boom is a shock wave produced when an object travels faster than the speed of sound
  • Occurs when aircraft exceed Mach 1 (supersonic speed)
  • Can cause disturbances and damage to structures on the ground
• Resonance is the tendency of a system to oscillate at maximum amplitude at specific frequencies
  • Helmholtz resonators are used to amplify or absorb specific frequencies (musical instruments, acoustic filters)
  • Resonance can be harmful in structures (Tacoma Narrows Bridge collapse)
• Binaural beats are an auditory illusion created when two slightly different frequencies are played separately into each ear
  • The brain perceives a third frequency equal to the difference between the two original frequencies
  • Claimed to have various effects on mood, concentration, and relaxation (meditation, sleep aids)
• Acoustic levitation uses high-intensity sound waves to suspend objects in mid-air
  • Achieved by creating standing waves with nodes that can trap small objects
  • Potential applications in containerless processing, micro-manipulation, and space exploration