17.1 Sound Waves

Sound waves are mechanical disturbances that travel through matter. They're characterized by properties like frequency, wavelength, and amplitude. Understanding these properties helps us grasp how sound behaves in different media and situations.

Sound waves create alternating regions of compression and rarefaction as they move. This process is key to how sound travels and interacts with its environment. We'll explore equations that describe wave propagation and dive into advanced phenomena like resonance and interference.

Properties and Behavior of Sound Waves

Sound vs hearing distinction

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• Sound physical phenomenon involves mechanical waves propagating through medium
  • Vibrations create alternating regions of compression and rarefaction (gases, liquids, solids)
• Hearing sensory perception occurs when sound waves interact with ear
  • Ear detects sound waves and converts them into electrical signals
  • Brain interprets signals allowing perception of sound characteristics (pitch, loudness, timbre)

Properties of sound waves

• Sound waves are longitudinal waves
  • Particles in medium oscillate parallel to direction of wave propagation
  • Contrast with transverse waves particles oscillate perpendicular to direction of wave propagation
• Properties of sound waves include:
  • Frequency ($f$) number of oscillations per unit time measured in hertz (Hz)
  • Wavelength ($\lambda$) distance between two consecutive points in same phase of wave measured in meters (m)
  • Amplitude maximum displacement of particles from equilibrium position related to loudness of sound
  • Speed ($v$) rate at which wave propagates through medium measured in meters per second (m/s)
  • Sound intensity: amount of energy transported by sound waves per unit area per unit time
• Sound wave behavior in various media:
  • Gases sound waves travel faster in less dense gases and slower in more dense gases (helium vs air)
  • Liquids sound waves generally travel faster than in gases due to closer proximity of particles (water vs air)
  • Solids sound waves travel fastest due to strong intermolecular forces and close packing of particles (steel vs water)

Equations for wave propagation

• Wave equation $v = f \lambda$
  • Relates speed ($v$) frequency ($f$) and wavelength ($\lambda$) of wave
  • Calculate any of three variables when other two are known (find wavelength given speed and frequency)
• Speed of sound in gases $v = \sqrt{\frac{\gamma R T}{M}}$
  • $\gamma$ ratio of specific heats (1.4 for diatomic gases like air)
  • $R$ universal gas constant (8.314 J/mol·K)
  • $T$ absolute temperature in kelvins (K)
  • $M$ molar mass of gas (kg/mol)
• Doppler effect $f_o = f_s \frac{v \pm v_o}{v \mp v_s}$
  • $f_o$ observed frequency
  • $f_s$ source frequency
  • $v$ speed of sound in medium
  • $v_o$ speed of observer (positive if moving towards source negative if moving away)
  • $v_s$ speed of source (positive if moving away from observer negative if moving towards)

Compression and rarefaction in sound

• Compression region in sound wave where particles are closer together than equilibrium position
  • Higher pressure and density compared to surrounding medium
• Rarefaction region in sound wave where particles are farther apart than equilibrium position
  • Lower pressure and density compared to surrounding medium
• Role in sound transmission:
  1. As sound wave propagates it creates alternating regions of compression and rarefaction
  2. These regions cause pressure variations in medium which transmit sound energy from one point to another
  3. Motion of particles in medium is parallel to direction of wave propagation resulting in longitudinal wave (air molecules in flute)

Advanced Sound Phenomena

• Acoustics: study of sound production, transmission, and effects in various environments
• Resonance: amplification of sound waves when driving frequency matches natural frequency of an object or system
• Interference: interaction of multiple sound waves, resulting in constructive or destructive effects
• Standing waves: stationary wave patterns formed by interference of waves traveling in opposite directions
• Harmonics: integer multiples of fundamental frequency in a vibrating system, contributing to timbre
• Decibel: logarithmic unit used to measure sound intensity levels relative to a reference intensity