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General doppler eqn.
f'=(v+v_o)/(v-v_s)f
Sonic boom
sin(theta)=v/v_s
Angular frequency
(omega)=2(pi)f
Wave number
k=2(pi)/(lambda)
Velocity of wave propagation (string)
v=sqrt(T/(mu))
Power of wave
P=1/2(mu)(omega)^2A^2v
Sound level
(beta)=10log(I/I_o)
General wave eqn.
y(x,t)=A*sin(kx-(omega)t+(phi))
Helpful trig. identity
sin(a)+sin(b)=2cos((a-b)/2)sin((a+b)/2)
Threshold of hearing
I_0=1.00*10^(-12)W/m^2
Threshold of pain
I=1.00W/m^2
Density of air
(rho)=1.20kg/m^3
Velocity of sound wave through medium
v=sqrt(B/rho)
Speed of wave oscillaitons
v=dx/dt=(omega)A*cos(kx-(omega)t+(phi))
Beats
f_beat=|f_1-f_2|
Natural frequencies of string fixed at both ends
f_n=n/(2L)sqrt(T/(mu)) n=1,2,3,...
Natural frequencies of a column of air open at both ends
f_n=n*v/(2L) n=1,2,3,...
Natural frequencies of a column of air open at one end and closed at the other
f_n=n*v/(4L) n=1,3,5,...
Standing wave eqn.
y=(2A*sin(kx))cos((omega)t)
Sound wave's variation in pressure
(Delta)P=(Delta)P_max*sin(kx-(omega)t)
Sound wave's variation in position
s(x,t)=s_max*cos(kt-(omega)t)
Relationship between pressure and displacement
(Delta)P_max=(rho)v(omega)s_max
Power Units
W=J/s
mu units
kg/m
Period of simple pendulum
T=2(pi)sqrt(L/g)
Period of oscillation
T=2(pi)/(omega)=2(pi)sqrt(m/k)
Total energy of a simple harmonic oscillator
E=1/2*kA^2
Units of (omega)
(omega)=f=s^(-1)
Units of spring constant
k=N/m
Doppler shift: observer approaching source
f'=[(v+v_o)/v]f
Doppler Shift: observer retreats from source
f'=[(v-v_0)/v]f
Doppler Shift: source approaches observer
f'=[v/(v-v_s)]f
Doppler Shift: source retreats from observer
f'=[v/(v+v_s)]f
Relationship of intensity and distance
I=P/[4(pi)r^2]
Speed of sound in relation to temperature
v=(331m/s)sqrt(1+T/273C)
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