physics 53 lecture dr. brown 30 november 2010 waves on a string -- review -- transmit energy consider small pulse in string...apply N2...derive one dimensional wave equation guess solution...show it works for general function of [ x \pm v t ] general solution is superposition of wave propogating to the right and the left... most/many interesting particular solutions involve Harmonic waves! solution of form: y(x,t) = y_o sin(kx \pm \omega t) k \lambda = 2 \pi \omega T = 2 \pi v = \omega / k = \lambda / T = frequency * \lambda energy transport and power and intensity of wave [only conservative forces] total kinetic energy 1/2 \delta m v_y^2 got total energy, average power -- defined energy density done with waves on string E&M waves {light} c= 3 x 10^8 Sound Waves -- details bit tougher [longitudinal waves...] velocity of sound in air @ room temp = 340 m/s pressure or displacement description Intensity = P_average/unit area= P_averge/{4 \pi r^2} sound intensity varies by factors of 10 and we use logarithmic scale with units in decibels I_o = 10^-12 Watts/m^2 threshold of hearing D(decibels) = 10 dB log {I/I_o} dimensionless scale for sound intensity