🌊College Physics II – Mechanics, Sound, Oscillations, and Waves Unit 17 – Sound: Waves, Properties, and Perception

Key Concepts

• Sound is a longitudinal wave that propagates through a medium by compressing and rarefacting particles
• Characteristics of sound waves include frequency, wavelength, amplitude, and speed
• Properties of sound waves such as reflection, refraction, diffraction, and interference affect how sound behaves in different environments
• Sound production involves vibrating objects that create pressure variations in the surrounding medium
• Sound propagation depends on the properties of the medium, such as density and elasticity
• Human perception of sound involves the ear converting pressure variations into electrical signals interpreted by the brain
• Applications of sound principles are found in music, acoustics, ultrasound imaging, and noise reduction technologies
• Common misconceptions about sound include the idea that sound can travel through a vacuum and that sound always travels at the same speed regardless of the medium

Wave Characteristics of Sound

• Sound waves are longitudinal waves that cause particles in a medium to oscillate parallel to the direction of wave propagation
• Frequency of a sound wave determines its pitch, with higher frequencies corresponding to higher-pitched sounds and lower frequencies corresponding to lower-pitched sounds
  • The human ear can typically hear frequencies between 20 Hz and 20 kHz
• Wavelength of a sound wave is the distance between two consecutive compressions or rarefactions and is inversely proportional to the frequency
• Amplitude of a sound wave determines its loudness, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to quieter sounds
  • Amplitude is related to the amount of energy carried by the wave
• Speed of sound depends on the properties of the medium, such as temperature and density
  • In air at room temperature (20°C), the speed of sound is approximately 343 m/s
• Sound waves exhibit properties such as reflection, refraction, diffraction, and interference, which affect how sound behaves in different environments

Properties of Sound Waves

• Reflection occurs when a sound wave encounters a boundary between two media and bounces back, following the law of reflection
  • Echoes are an example of sound reflection
• Refraction occurs when a sound wave passes from one medium to another with a different density, causing the wave to change direction
  • This can be observed when sound travels from air to water or vice versa
• Diffraction is the bending of sound waves around obstacles or through openings, allowing sound to propagate around corners and through small spaces
  • The amount of diffraction depends on the size of the obstacle or opening relative to the wavelength of the sound
• Interference occurs when two or more sound waves overlap, resulting in constructive (increased amplitude) or destructive (decreased amplitude) interference
  • Beats are an example of interference between two sound waves with slightly different frequencies
• The Doppler effect is the change in the observed frequency of a sound wave when the source or observer is moving relative to each other
  • This effect is noticeable in the change of pitch of a siren as an emergency vehicle passes by
• Sound intensity is the power carried by a sound wave per unit area and is related to the amplitude of the wave
  • Sound intensity level is measured in decibels (dB) and is a logarithmic scale

Sound Production and Sources

• Sound is produced by vibrating objects that create pressure variations in the surrounding medium
  • Examples of sound sources include musical instruments, human vocal cords, and loudspeakers
• Vibrations can be created by various mechanisms, such as plucking a string, striking a membrane, or forcing air through a reed
• The characteristics of the sound produced depend on the properties of the vibrating object, such as its size, shape, and material
• Resonance occurs when a sound source vibrates at its natural frequency, resulting in increased amplitude and efficiency of sound production
  • Musical instruments rely on resonance to amplify and shape their sound
• Harmonics are integer multiples of the fundamental frequency and contribute to the timbre or quality of a sound
  • Different combinations of harmonics give different sound sources their unique characteristics
• Noise is an irregular or random sound that lacks a clear pitch or frequency structure
  • White noise contains equal power across all frequencies, while pink noise has more power at lower frequencies

Sound Propagation and Medium

• Sound waves require a medium to propagate, as they are mechanical waves that involve the oscillation of particles
  • Sound cannot travel through a vacuum, as there are no particles to oscillate
• The speed of sound depends on the properties of the medium, such as its density, temperature, and elasticity
  • In general, sound travels faster in solids than in liquids, and faster in liquids than in gases
• The speed of sound in air increases with temperature, as higher temperatures lead to increased particle velocity and more frequent collisions
  • The relationship between temperature and speed of sound in air is given by: $v = 331 + 0.6T$, where $v$ is the speed in m/s and $T$ is the temperature in °C
• Sound waves can be attenuated or weakened as they propagate through a medium due to absorption, scattering, and spreading
  • Absorption occurs when sound energy is converted into heat due to the viscosity and thermal conductivity of the medium
  • Scattering occurs when sound waves encounter obstacles or inhomogeneities in the medium and are redirected in various directions
  • Spreading refers to the decrease in sound intensity as the wave propagates outward from the source, following an inverse square law

Human Perception of Sound

• The human ear is the primary organ responsible for detecting and processing sound waves
  • The outer ear collects and funnels sound waves to the eardrum, which vibrates in response to the pressure variations
  • The middle ear contains three small bones (ossicles) that amplify and transmit the vibrations to the inner ear
  • The inner ear contains the cochlea, a fluid-filled structure lined with hair cells that convert the mechanical vibrations into electrical signals
• The brain interprets the electrical signals from the ear to create the perception of sound, including pitch, loudness, and timbre
• Pitch perception is related to the frequency of the sound wave, with higher frequencies corresponding to higher-pitched sounds
  • The human ear is most sensitive to frequencies between 2 kHz and 5 kHz, which is important for understanding speech
• Loudness perception is related to the amplitude of the sound wave and is measured in decibels (dB)
  • The human ear can detect sounds with intensities ranging from 0 dB (threshold of hearing) to 120 dB (threshold of pain)
• Timbre is the quality of a sound that distinguishes it from other sounds with the same pitch and loudness
  • Timbre is determined by the relative amplitudes and phases of the harmonics present in the sound
• Localization is the ability to determine the direction and distance of a sound source based on binaural cues (differences in time and intensity between the two ears) and spectral cues (changes in the frequency content of the sound due to the shape of the outer ear)

Applications and Real-World Examples

• Acoustics is the study of sound and its behavior in various environments, such as concert halls, recording studios, and outdoor spaces
  • Acoustic design involves controlling the reflection, absorption, and diffusion of sound to create desired sound characteristics and minimize unwanted noise
• Ultrasound is sound with frequencies above the human hearing range (>20 kHz) and has numerous applications in medicine, industry, and research
  • Medical ultrasound imaging uses high-frequency sound waves to create images of internal body structures, such as fetuses during pregnancy
  • Industrial ultrasound is used for non-destructive testing, cleaning, and welding of materials
• Sonar (Sound Navigation and Ranging) is a technique that uses sound waves to detect and locate objects underwater
  • Active sonar emits sound pulses and listens for echoes, while passive sonar listens for sounds emitted by the objects themselves
• Noise reduction and cancellation technologies use principles of sound interference and absorption to minimize unwanted noise in various settings
  • Active noise cancellation headphones generate sound waves that destructively interfere with ambient noise, effectively canceling it out
  • Sound-absorbing materials, such as acoustic foam and fiberglass insulation, are used to reduce echoes and reverberation in rooms
• Music and speech rely heavily on the principles of sound production, propagation, and perception
  • Musical instruments are designed to produce specific frequencies and timbres through various mechanisms, such as vibrating strings, air columns, and membranes
  • Speech production involves the coordinated use of the vocal cords, tongue, and lips to create distinct sounds and words

Common Misconceptions and FAQs

• Misconception: Sound can travel through a vacuum
  • Reality: Sound requires a medium to propagate and cannot travel through a vacuum, as there are no particles to oscillate
• Misconception: Sound always travels at the same speed, regardless of the medium
  • Reality: The speed of sound depends on the properties of the medium, such as density, temperature, and elasticity, and can vary significantly between different materials
• Misconception: Higher pitch means higher speed
  • Reality: Pitch is determined by the frequency of the sound wave, not its speed. The speed of sound is independent of its frequency or pitch
• FAQ: What is the difference between sound and light?
  • Sound is a mechanical wave that requires a medium to propagate, while light is an electromagnetic wave that can travel through a vacuum. Sound travels much slower than light and has a lower frequency range
• FAQ: Can humans hear ultrasound?
  • Humans cannot hear ultrasound, as our hearing range is limited to frequencies between 20 Hz and 20 kHz. However, some animals, such as bats and dolphins, can detect and use ultrasound for navigation and communication
• FAQ: How does sound insulation work?
  • Sound insulation works by using materials that absorb, reflect, or dampen sound waves, reducing their transmission through walls, floors, and ceilings. Common sound insulation materials include fiberglass, foam, and mass-loaded vinyl
• FAQ: Why do sound waves get weaker as they travel?
  • Sound waves get weaker as they travel due to attenuation, which includes absorption (conversion of sound energy into heat), scattering (redirection of sound waves by obstacles), and spreading (decrease in intensity as the wave propagates outward from the source)