Chs. 13-14 Flashcards
Simple Harmonic Motion: Force of Spring
Fs= -kx
Simple Harmonic Motion: acceleration
a = -kx/m
Elastic Potential Energy
PE = 1/2 kx^2
Velocity with simple harmonic motion
v = +/- √k/m (A^2-x^2)
Period of an object moving with simple harmonic motion
T = 2π√m/kj
Frequency of an object-spring system
ƒ= 1/T ƒ= 1/2π√k/m
Angular Frequency
omega = 2πƒ = √k/m
Position of an object in simple harmonic motion
x = Acos (2πƒt)
Velocity of an object in simple harmonic motion
v = -A omega sin (2πƒt)
Acceleration of an object in simple harmonic motion
a = -A omega^2 cos (2πƒt)
Maximum Velocity of an object in simple harmonic motion
v = Aomega
Maximum Acceleration of an object in simple harmonic motion
a = A omega^2
Period of a simple pendulum
2π√L/g
Transverse Wave
the elements of the medium move in a direction perpendicular to the direction of the wave; a wave on a stretched string
Longitudinal Wave
elements of the medium move parallel to the direction of the wave velocity; a sound wave
Velocity and Wavelength
v = ƒλ
Speed of Waves on Strings
v = √F/(M/L)
Superposition Principle
if two or more traveling waves are moving through a medium, the resultant wave is found by adding the waves together point by point
Speed of Sound in a fluid
v = √B/ ρ B = bulk modulus
Speed of a longitudinal wave in a solid rod
v = √Y/ ρ
Speed of sound in air
v= 331√T/273
Intensity of a wave
I = P/A P = sound power
Relative Intensity of sound (the intensity we hear sounds)
β = 10 log (I / Ii)
Ii = 1.0 x 10^-12 (sound at threshold of hearing)
given in decibels
Intensity of a Spherical Wave; intensity of a sound at a distance away
I = Pav/4πr^2
Ratio of intensities at two different distances away
I1/I2 = r2^2/r1^2
Doppler Effect: when the observer is moving relative to a stationary source
ƒo = ƒs ((v + vo)/v)
Doppler Effect: when the source is moving relative to the observer
ƒo = ƒs (v/(v-vs))
Doppler Effect: General Case
ƒo = ƒs ((v+vo)/(v-vs))
Mach Number
Ratio between speed of object and speed of sound
Constructive Interference Equation
r2 - r1 = n λ
Destructive Interference Equation
r2 - r1 = (n + 1/2) λ
Fundamental Frequency (and thus following frequencies)
ƒn = nƒ1 = n/2L √F/(M/L) n = 1, 2, 3 (harmonics)
Second Harmonic Description on a String
Length of String = λ
2 antinodes
3 nodes
Third Harmonic Description: String
L = 3/2 λ
4 nodes
3 antinodes
Fourth Harmonic Description: String
L = 2 λ
5 nodes
4 antinodes
First Harmonic Description: String
L = 1/2 λ
2 nodes
1 antinodes
First Harmonic Description: open-end air column
L = 1/2 λ
1 node
2 antinodes
Second Harmonic: open-end air column
L = λ
2 nodes
3 antinodes
Third Harmonic: open-end air column
L = 3/2 λ
3 nodes
4 antinodes
Frequency of open end air columns
ƒ = n (v/2L) = nƒ1 n = harmonic
Frequency of closed end air column
ƒ = n (v/4L) = nƒ1
First Harmonic: closed-end air column
L = 1/4 λ
1 node
1 antinode
Third Harmonic: closed end air column
L = 3/4 λ
2 nodes
2 antinodes
Fifth Harmonic: closed end air column
L = 5/4 λ 3 nodes 3 antinodes (remember, closed end air columns have no even harmonics)
Frequency of a Beat
ƒb = ƒ2 - ƒ1
