Physics and Math 7 Waves and Sound

Physics and Math 7: Waves and Sound Sound Sound: Produced by mechanical disturbance of a material that creates an oscillation of the molecules in the material. Propagation: Sound propagates through all forms of matter but not through a vacuum. Fastest through solids, followed by liquids, and slowest through gases. Within a medium, as density increases, speed of sound decreases. General Wave Characteristics Transverse Waves: Have oscillations of wave particles perpendicular to the direction of wave propagation. LIGHT Longitudinal Waves: Have oscillations of wave particles parallel to the direction of wave propagation. SOUND 𝑣 =#𝑓#l 7 𝑣 =# r 𝑣# =wave#speed 𝑓# =frequency l #=wavelength 𝐵#=#bulk#modulus (increases from gas to liquid to solid) r #=density Displacement (x): Refers to how far a point is from the equilibrium position, expressed as a vector quantity. Amplitude (A): The magnitude of its maximal displacement. The maximum point is called a crest. The minimum point is called a trough. Wavelength ( l ): The distance between two crests or two troughs. Frequency (f): The number of cycles it makes per second. Expressed in Hz. Pitch: Our perception of frequency. Doppler Effect: A shift in the perceived frequency of a sound compared to the actual frequency of the emitted sound when the source of the sound and its detector are moving relative to one another. The apparent frequency will be higher than the emitted frequency when the source and detector are moving toward each other. The apparent frequency will be lower than the emitted frequency when the source and detector are moving away from each other. The apparent frequency can be higher, lower, or equal to the emitted frequency when the two objects are moving in the same direction, depending on their relative speeds. F#±F Angular Frequency (w ): Also known as radial or circular frequency, measures angular displacement per unit time. ?#p Expressed in radians per second. w#=2# p #𝑓 = @ Period (T): The number of seconds it takes to complete a B cycle. It is the inverse of frequency. #𝑇# =#C Interference: Describes the ways in which waves interact in space to form a resultant wave. Constructive Occurs when waves are exactly in phase with each Interference: other. The amplitude of the resultant wave is equal to the sum of the amplitudes of the two interfering waves. Destructive Occurs when waves are exactly out of phase with Interference: each other. The amplitude of the resultant wave is equal to the difference in amplitude between the two interfering waves. Partially Constructive / Occurs when two waves are not quite perfectly in Destructive Interference: or out of phase with each other. The displacement 𝑓 D =#𝑓#(F#∓F H) J 𝑓 D =#percieved#freq 𝑓=#emitted#freq Use the Top sign for “toward”, bottom sign for “away” Intensity: Intensity is related to a wave’s amplitude. Intensity decreases over distance and some energy is lost to attenuation from frictional forces. 𝐼= M N 𝑃#= #power 𝐴=#area Strings and Support standing waves and the length of the string or Open Pipes: pipe is equal to some multiple of half-wavelengths. R#l 𝐿 =# ##( 𝑛 = 1,2,… ) ? Closed Pipes: Closed at one end. Support standing waves, and the length of the pipe is equal to some odd multiple of quarterR#l wavelengths. 𝐿 =# W ## ( 𝑛 = 1,3,… ) Ultrasound: Uses high frequency sound waves to compare the relative densities of tissues in the body. Doppler Ultrasound is used to determine the flow of blood within the body. of the resultant wave is equal to the sum of the displacements of the two interfering waves. Traveling Waves: Have continuously shifting points of maximum and minimum displacement. Standing Waves: Produced by the constructive and destructive interference of two waves of the same frequency traveling in opposite directions in the same space. Antinodes: Points of maximum oscillation. Nodes: Points where there is no oscillation. Resonance: The increase in amplitude that occurs when a periodic force is applied at the natural (resonant) frequency. Damping: A decrease in amplitude caused by an applied or nonconservative force. 1st, 2nd, and 3rd Harmonics of a String: N = node, A = antinode. As a shortcut, for strings attached at both ends, the number of antinodes present will tell you which harmonic it is