Chapter 16: Sound and Hearing

The fundamental nature of sound is explored through its frequency-dependent properties, including the audible range of human hearing from 20 Hz to 20,000 Hz, with infrasonic waves below this range and ultrasonic waves above it. The chapter develops mathematical models for sound wave propagation, establishing that the speed of sound depends on the elastic properties and density of the medium, with specific formulations for fluids using bulk modulus, solids using Young's modulus, and gases incorporating temperature and molecular mass effects. Sound intensity is analyzed as the energy flux per unit area, introducing the decibel scale as a logarithmic measure of sound level relative to the threshold of hearing, and demonstrating how intensity follows the inverse square law with distance. The formation of standing wave patterns in both open and stopped pipes is examined, revealing how boundary conditions determine the allowed frequencies and harmonic series, with open pipes supporting all integer multiples of the fundamental frequency while stopped pipes only support odd harmonics. The chapter explores resonance phenomena where systems exhibit maximum response at natural frequencies, and beat formation resulting from the interference of two waves with slightly different frequencies. The Doppler effect is thoroughly analyzed, showing how relative motion between source and observer creates frequency shifts, with mathematical expressions for various motion scenarios. Finally, the chapter addresses supersonic motion and shock wave formation, introducing the Mach number and explaining how objects exceeding the speed of sound create cone-shaped pressure disturbances that produce sonic booms.