Ch. 8 Periodic motion, Waves, Sound
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| Hooke's Law | F=-kx
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| acceleration of a spring with constant k and mass m, having been displaced x meters | a=-w^2x, w=angular frequency. w=2pif=(k/m)^1/2 w is measured in radians per second,
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| what does frequency/angular frequency depend on | the spring constant and the mass attached to the spring, but not on the displacement of the spring
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| kinetic and potential energy for springs | U=1/2kx^2 K=1/2mv^2
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| restoring force of pendulum | F=-mgsin(theta)
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| angular frequency of pendulum | w=2pif=(g/L)^1/2 only the acceleration of gravity and the length of the pendulum affect angular frequency
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| pendulum max potential energy | U=mgh h is the vertical height difference between the pendulum's mass in the equilibrium position and mass at the given angular displacement
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| longitudinal waves | particles of the wave oscillate along the direction of travel of the wave motion; the wave particles are oscillation along the direction of energy transfer.
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| transverse waves | particles are oscillating perpendicular to the direction of energy transfer
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| displacement of particle in a wave | y=Ysin(kx-wt) Y is amplitude, k is wave number, w is angular frequency
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| speed of wave v | v=(freq.)(lambda)
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| wave number and angular frequency | k=(2pi)/lambda w=2pif=(2pi)/T
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| what is speed of sound proportional too | inversely proportional to the square root of density but directly proportional to the square root of the bulk modulus.
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| Intensity | I=P/A SI units of W/m^2 A is surface area, also expressed as P=IA
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| What is intensity proportional too | the square of the amplitude. Doubling amplitude produces wave that is 4 times as intense. Intensity also related to distance from the source of sound wave.
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| decibels equation | B=10log(I/I.) I.=threshold of hearing 1x10^-14 W/m^2 ratio of two intensities can be found by Bf=Bi+log(If/Ii) where If/Ii is the ration of the final intensity of the initial intensity
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| doppler shifts | if source and detector moving toward each other, perceived freq f' is greater than actual frequency f, if moving away perceived frequency f' is less than actual freq.
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| standing wave equations | lambda=(2L/n) f=(nv/2L) n=1,2,3,...
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| what is the fundamental frequency | the lowest frequency (longest wavelength) of a standing wave that can be supported in a given length of string
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| pipes and standing waves (nodes and anodes) | if the end is open, it will support an antinode, if it is closed, it will support a node
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| open pipe wave equations | lambda=(2L/n) n=1,2,3,... f=v/f, f=(nv/2L)
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| closed pipe wave equations | lambda=(4L/n) n=1,3,5,.... f=(nv/4L)
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