Phy 202: General Physics II Ch 16: Waves & Sound Lecture Notes What are waves? Waves are traveling disturbances or vibrations Waves carry energy from place to place There are 2 types of waves: Transverse (example: light, electromagnetic waves) Disturbance is perpendicular to direction of wave propagation Longitudinal (example: sound waves) Disturbance is parallel to direction of wave propagation Properties of Periodic Waves All waves share 3 properties: The propagation speed of the wave, vwave The spacial length of a wave from crest to crest is called its wavelength,
The rate (or frequency) of vibration describes how fast a wave oscillates, f The propagation of a wave is related to its wavelength & its frequency: vwave = .f The speed of wave depends on the properties of the material (medium) where the wave travels. For a wave on a string: F v m/ L Where: F = tension in the string m = mass of the string L = length of the string Sound
Longitudinal wave Produced by vibrations in a medium The disturbance is the local change in pressure generated by the vibrating object It travels because of the molecular interactions. The region of increased pressure( compared to the undisturbed pressure) is called condensation The region of lower pressure is called rarefaction. The maximum increase in pressure is the amplitude of the pressure wave. (measurable) Frequency of the sound 20Hz to-20000Hz. Pressure waves below 20 Hz are called infrasonic waves Pressure waves over 20,000Hz are called ultrasonic waves. The Speed of Sound Speed of sound depends on the compressive properties of the medium. Because of the high frequencies, the compression/expansions are fast and no heat is exchanged (adiabatic). Sound can travel in gases, liquids and solids.
The speed of sound in gases: The speed of sound in liquids: The speed of sound in solids: kT v m0 Badiab v v Y Sound Intensity
Waves transport energy without transporting mass. The amount of energy transported per second is called the power of the wave (W) (power of the sound) The power of the wave is determined by the source. The power is distributed (spreads) in all directions. Far away from the source, the power is spread over a greater area. Intensity is a measure of power transmitted by a wave per unit area: I = P/A The human does not sense sound intensity linearly but rather logarithmically The decibel scale has been developed to linearize the human ear response to sound intensity = (10 dB) . log (I/Io) where Io is the minimum intensity of sound the average human ear can detect Doppler Effect The frequency of the source producing the wave equals the number of cycles per second. The frequency measured by an observer is the number of crests (condensations) encountered per second.
When both the source and the observer are at rest, the 2 frequencies are equal. When one or both are in motion, the 2 frequencies are different. The difference between source and observed frequency is called Doppler shift Doppler Shift (Moving source, observer at rest) The wavelength is changed because of the relative motion of source and observer Source moving toward observer f observer 1 fs 1 vs
v Notes: vs = speed of source v = speed of sound fs = frequency of source Source moving away from the observer f observer
1 fs 1 vs v Doppler Shift (Moving observer, source at rest) The time between encountering 2 crests changes for observer Observer moving toward source Notes:
v0 vo = speed of observer f observer f s 1 v Observer moving away from source f observer v0 f s 1 v v = speed of sound fs = frequency of source
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