Waves and Periodic Motion, Sound and Solids Flashcards
Formula for simple harmonic motion
X= Acosωt or X=Asinωt
Frequency Factor
ω; related to frequency but is no the frequency. Their relationship is proportional
Phase shift of a wave to the right
x= Acos(ωt-Ф); over all subtracting
Phase shift of a wave to the left
X=Acos(ωt+Ф); over all adding
The period (T) is
The duration of time for one given event in a group. T = 1/ƒ
The frequency (ƒ) is
The amount an event occurs in a given time ƒ = 1/T; measured in Hz
Formula for a spring
ω = √k/m “Whack em”
Formula for a pendullum
ω = √g/L “Wiggle”
Formula for Vmax in simple harmonic motion
Vmax = Aω
Formila for amax in simple harmonic motion
amax = Aω^2
When dealing with pendullum how does the mass of the object affect its period/frequency?
The mass is irrelevant
Hook’s Law
F = -kx
Formula for elastic potential energy
P.E. = (1/2)(kx^2)
How are the “pulling force” and the displacement in a spring related
They will point in the same direction
How are the “force of the spring” and the displacement of a spring related
They will point in opposite directions
At equilibrium a spring experiences
Only K.E. Vmax F = 0 a = 0
At the extremes a spring experinces
V = 0 a max K.E. = 0 X = A (max amplitude) Only P.E.
How are K.E. + P.E. Related to each other at the equilibrium position
They are equal to each other K.E. = P.E. (Elastic)
Longitudinal Waves
Medium moves in direction of the wave
Transverse waves
Medium moves perpendicular to the wave
Formula for velocity in relation to sound
λƒ = v Vsound = ~343 m/s
What is the order of medium (fastes -> slowest) in which sound travels
S > l > g Sound generally travels faster in solids than in liquids and gases
Formula for speed in sound in solids/liquids
V ∝ √1/ρ **Only use this to compare solids to solids or liquids to liquids**
Formula for speed in gases
V ∝ √P/ρ
Formula for standing waves in a pipe open at both ends or a rope with both ends fixed
λn = 2L/n n = 1,2,3..etc
Formula for standing waves in a pipe open at one end
λn = 4L/n n = odd #’s
n=1 is
The first harmonic or the fundamental frequency
Beat frequency
Difference between two frequencies of two different sound waves i.e. 190Hz - 180Hz = 10Hz is the Beat Frequency
Formula for Intensity
I = P/A = P/4πr^2
Every factor of 10x equals 10dB of intensity
10x loud = 10dB 100x = 20dB 1000x = 30 dB
Formula for intensity level (not intensity)
β = 10log(I/Io)
Lowest intensity humans can hear
Io = 10^-12 (W/m^2)
Doppler Effect formula
ƒo = ƒs (V ± Vo/ V ± Vs)
ƒo > ƒs
Object and source are moving towards each other
ƒo < ƒs
Object and source are moving away from each other
If possible calculate the percentage of wavelengths in respect to the speed of sound
i.e. (343 m/s)/(15 m/s) ~ 22% change
Young’s Modulus for stretching and compressing
F/A = Y (ΔL/Lo)
Shear Modulus for Shear Defromation (tilting of a large book)
F/A = S (ΔX/Lo)
Bulk Modulus for Volume Deformation
ΔP = -B (ΔV/Vo)
Overtones
efficiency of heat formula
e = 1 - (Tc/Th)
First harmonic formula
f1 = nv/4L (pipe open at one end)
f1 = nv/2L (pipe open at both ends)
Frequency of a wave when you aren’t given the speed
f = # cycles/time
Formula for period of a pendullum
T= 2π√1/g
