Section 14.2: Characteristics of Sound Waves Sound waves are longitudinal waves. Audible waves are sound waves with frequencies between 20 and 20 000 Hz. Infrasonic waves have frequencies below the audible range, and ultrasonic waves have frequencies above the audible range. Section 14.3: The Speed of Sound The speed of sound in a medium of bulk modulus B and density _{} is The speed of sound also depends on the temperature of the medium. The relationship between temperature and the speed of sound in air is where T is the absolute (Kelvin) temperature and 331 m/s is the speed of sound in air at 0°C. Section 14.4: Energy and Intensity of Sound Waves The average intensity of sound incident on a surface is defined by where the power _{} is the energy per unit time flowing through the surface, which has area A. The intensity level of a sound wave is given by The constant I_{0} = 1.0 x 10^{12} W/m^{2} is a reference intensity, usually taken to be at the threshold of hearing, and I is the intensity at level _{}, measured in decibels (dB). Section 14.5: Spherical and Plane Waves The intensity of a spherical wave produced by a point source is proportional to the average power emitted and inversely proportional to the square of the distance from the source: Section 14.6: The Doppler Effect The change in frequency heard by an observer whenever there is relative motion between a source of sound and the observer is called the Doppler effect. If the observer is moving with speed v_{O} and the source is moving with speed v_{S}, the observed frequency is where v is the speed of sound. A positive speed is substituted for v_{O} when the observer moves toward the source, a negative speed when the observer moves away from the source. Similarly, a positive speed is substituted for v_{S} when the source moves toward the observer, a negative speed when the source moves away. Section 14.7: Interference of Sound Waves When waves interfere, the resultant wave is found by adding the individual waves together point by point. When crest meets crest and trough meets trough, the waves undergo constructive interference, with path length difference When crest meets trough, destructive interference occurs, with path length difference Section 14.8: Standing Waves Standing waves are formed when two waves having the same frequency, amplitude, and wavelength travel in opposite directions through a medium. The natural frequencies of vibration of a stretched string of length L, fixed at both ends, are where F is the tension in the string and _{} is its mass per unit length. Section 14.9: Forced Vibrations and Resonance A system capable of oscillating is said to be in resonance with some driving force whenever the frequency of the driving force matches one of the natural frequencies of the system. When the system is resonating, it oscillates with maximum amplitude. Section 14.10: Standing Waves in Air Columns Standing waves can be produced in a tube of air. If the reflecting end of the tube is open, all harmonics are present and the natural frequencies of vibration are If the tube is closed at the reflecting end, only the odd harmonics are present and the natural frequencies of vibration are Section 14.11: Beats The phenomenon of beats is an interference effect that occurs when two waves with slightly different frequencies combine at a fixed point in space. For sound waves, the intensity of the resultant sound changes periodically with time. The beat frequency is where f_{2} and f_{1} are the two source frequencies.
