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