Exam 1 Flashcards
Density formula
ρ = m/V
SI Unit of Density
1 kg/m^3 (also equals 1 g/cm^3)
Density of Air (kg/m^3)
1.20 kg/m^3
Density of Water (kg/m^3)
1.00 * 10^3 kg/m^3
Pressure formula
p = F/A
SI Unit of Pressure
1 Pascal = 1 Pa = 1 N/m^2
Atmospheric Pressure
1 atm = 101.325 kPa
Pressure at Depth Formula
ρ = patm + ρgh
Pascal’s Principle of Hydrostatics
A pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.
Gauge Pressure Formula
p-patm = ρgh
Archimedes’s Principle
When a body is completely or partially submerged in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.
Continuity Equation Formula
A1v1 = A2v2
Volume Flow Rate Formula
dV/dt = Av
Bernoulli’s Equation
p + ρgy + (1/2)ρv^2 = constant
Frequency Formula
f = 1/T
Angular Frequency Formula
ω = 2πf = (2*π)/T = rad(k/m) = rad(g/L)
Restoring Force of Ideal Springs
Fx = -k*x
Simple Harmonic Motion Displacement Formula
x(t) = Acos(ωt+ϕ)
Simple Harmonic Motion Velocity Formula
v(t) = -ωAsin(ωt+ϕ)
Simple Harmonic Motion Acceleration Formula
a(t) = -ω^2*Acos(ωt+ϕ)
Arc Length Formula
x = L*θ
Force Constant Substitute Formula
k = (mg)/L = (2π/T)^2I
SHM Period Formula
T = 2πrad(L/g)
Physical Pendulum Period Formula
T = 2πrad(I/(mgd)) where d is distance to COG
Physical Pendulum Acceleration Formula
a(t) = (-mgd)/I * θ
Transverse Wave
A wave where the displacement of the medium is perpendicular to the travel of the wave, i.e. wave on string.
Longitudinal Wave
A wave where the displacement of the medium is parallel to the travel of the wave, i.e. sound wave.
Wave Speed Formula
v = λ*f = ω/k
Wave Displacement Function for a Sinusoidal Wave
y(x,t) = Acos(kx±ωt) = Acos[2π(x/λ±t/T)]
Opposite Symbol in terms of the velocity, so +v dir. subtracts while -v dir. adds.
What is A?
Amplitude (m)
What is the spatial frequency (k)?
Wave Number (k) = (2*π)/λ
Wave Acceleration Function for a Sinusoidal Wave
a = -ω^2*y
Wave Velocity Formula for a Sinusoidal Wave
v = rad(Ftension/μ)
Linear Mass Density Formula
μ = m/L
Average Power for a Sinusoidal Wave Formula
Pav = (1/2)rad(μF)ω^2A^2
Maximum Power for a Sinusoidal Wave Formula
Pmax = 2*Pav
Fundamental Mode of a Stationary Wave
L = λ/2
Overtone Formula
λn = (2*L)/n
Wave Intensity Formula
I = P/Area
Frequency of Overtone Formula
fn = nf1
Fundamental Frequency Formula
f1 = (1/2L)*rad(F/μ)
Overtone to Harmonic
Harmonic = Overtone - 1
Pressure of Sound Wave Formula
P(x,t) = BkAsin(kx-ωt)
Maximum Pressure of Sound Wave Formula
Pmax = BkA
Velocity of Sound Wave in Fluid
v = rad(B/ρ)
Velocity of Sound Wave in Solid
v = rad(Y/ρ) where Y = stress/strain
Velocity of Sound Wave in Gas
v = rad(γRT/M) where R = Ideal Gas Constant = 8.314 J/molK T = Tc + 273 M = Molar Mass γ = 1.4 diatomic, 1.6 monotomic
Intensity of a Sound Wave Formula
I=Pmax/Area = Pm^2/(2ρv) = Pm^2/(2rad(ρB))
Intensity of a Sound Wave in Decibels Formula
β(dB) = 10*log(I/I0) where I) = Izero
What is I0 (Izero)?
I0 (Izero) = 10^-12 W/m^2
Open Pipe Frequency Formula
fn = (nv)/(2L)
Closed Pipe Frequency Formula
fn = (nv)/(4L)
Doppler’s Effect Formula
fo = (v±vL)/(v±vs)*fs
where
Top: + if listener is approaching source
Bottom: - if source is approaching listener
