physics 53 lecture dr. brown 2 december 2010 ****** review power and intensity for mechanical waves intensity is the power per unit area by a wave point source radiating out in all dimensions -- I = \frac{P_{av}}{4 \pi r^2} at some distance r from the source sun intensity at the equator is approx. 1000 W/m^2, knowing the distance to the sun allows us to calculate the average power produced by the sun :) ***** next - need a way to describe the intensity -- ear is sensitive to WIDE range of sound intensity ; eye is sensitive to WIDE range of light intensity -- therefore use a log scale \Beta = 10 \log{\frac{I}{I_o}} threshold of hearing I_o = 10^{-12} W/m^2 --- \Beta_o = 0 speaking-- conversation approx 60 dB ****** Pulse in string hits string of greater \mu [linear mass density]... transmitted and reflected pulse [inverted] pulse in string hits string of lesser \mu transmitted and reflected pulse [upright] ***** Doppler shift use amplitude peaks [wave fronts] to visualize \lambda_o = v T moving source or moving reciever or both... f' = f_o [ \frac{v \pm v_r}{v \mp v_s}] v_s velocity of the source relative to medium v_r velocity of the receiver relative to medium v velocity of the wave in medium ***** superposition principle proves any linear combination of solution to the wave equation also solves the wave equation