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# MCAT Physics

### Ch. 8 Periodic motion, Waves, Sound

Hooke's Law F=-kx
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,
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
kinetic and potential energy for springs U=1/2kx^2 K=1/2mv^2
restoring force of pendulum F=-mgsin(theta)
angular frequency of pendulum w=2pif=(g/L)^1/2 only the acceleration of gravity and the length of the pendulum affect angular frequency
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
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.
transverse waves particles are oscillating perpendicular to the direction of energy transfer
displacement of particle in a wave y=Ysin(kx-wt) Y is amplitude, k is wave number, w is angular frequency
speed of wave v v=(freq.)(lambda)
wave number and angular frequency k=(2pi)/lambda w=2pif=(2pi)/T
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.
Intensity I=P/A SI units of W/m^2 A is surface area, also expressed as P=IA
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.
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
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.
standing wave equations lambda=(2L/n) f=(nv/2L) n=1,2,3,...
what is the fundamental frequency the lowest frequency (longest wavelength) of a standing wave that can be supported in a given length of string
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
open pipe wave equations lambda=(2L/n) n=1,2,3,... f=v/f, f=(nv/2L)
closed pipe wave equations lambda=(4L/n) n=1,3,5,.... f=(nv/4L)