Oscillations and Waves

Question 1

Amplitude, A, and units

Answer 1

max displacement from eqlbm (max value of |x|)

units is metres

Question 2

Period, T, and units

Answer 2

time it takes to complete one cycle - always positive

units is seconds per cycle

Question 3

frequency, f, and units

Answer 3

number of cycles in a unit of time

unit is hertz

Question 4

angular frequency eqn

Answer 4

ω = 2πf
= 2π/T

Question 5

period is a reciprocal of…

Answer 5

frequency

Question 6

Simple Harmonic Motion

Answer 6

when restoring force is directly proportional to the displacement of eqlbm

Question 7

restoring force exerted by an ideal spring

Answer 7

F_x = -kx

k = force constant of spring
x = displacement

units of k are N/m or kg/s^2

Question 8

equation for SHM displacement

Answer 8

x = Acos(ωt +φ)

A= amplitude
ω = angular frequency
t = time
φ= phase angle
x = displacement

Question 9

displacement and acceleration always have…

Answer 9

opposite signs

Question 10

acceleration eqn, a_x

Answer 10

a_x = -ω^2x

Question 11

angular speed equation/ angular frequency for SHM

Answer 11

ω^2 = k/m
ω = sqrt(k/m)

Question 12

frequency for SHM

Answer 12

f = 1/(2π)sqrt(m/k)

Question 13

larger mass means acceleration is…

Answer 13

lower and it takes longer time to complete cycle

Question 14

larger force constant k means…

Answer 14

it’s a stiffer spring and has a greater force, acceleration and has a quicker T per cycle

Question 15

total mechanical energy in SHM eqn

Answer 15

E = (1/2)(mv^2) + (1/2)(kx^2)
= (1/2)(kA^2)
= constant

E = total mechanical energy
m = mass
v = velocity
k = force constant
x = displacement
A = amplitude

Question 16

what’s v_x of an object at a given displacement x?

Answer 16

v_x = +/- sqrt(k/m) * sqrt(A^2-x^2)

k= force constant
m= mass
A= amplitude
x= displacement

Question 17

whats v_max?

Answer 17

v_max = ωA

Question 18

SHM w frictional damping force can be directly proportional to…

Answer 18

the velocity of the oscillating object

Question 19

displacement of oscillator when damped

Answer 19

x = Ae^[-(b/(2m))t]cos(ω’t +φ)

x = displacement
A = amplitude
e = exponential
b = damped constant
m = mass
t= time
ω’ = angular frequency when damped
φ = phase angle

Question 20

angular frequency when damped

Answer 20

ω’ = sqrt( k/m - b^2/(4m^2))

Question 21

the larger the value of b…

Answer 21

the more quickly the amplitude decreases

Question 22

when b = 2*sqrt(k/m)

Answer 22

critical damping so system no longer oscillates but returns to eqlbm position

Question 23

when b>2*sqrt(k/m)

Answer 23

overdamping

Question 24

when b < 2*sqrt(k/m)

Answer 24

underdamping

Question 25

total mechanical energy for damped oscillations

Answer 25

E = (1/2)mx^2 + (1/2)kx^2

Question 26

amplitude of a forced oscillator (damped)

Answer 26

A = F_max / sqrt [ (k-mw_d^2)^2 + b^2w_d^2] F_max = max value of driving force w_d = driving angular frequency

Question 27

transverse wave

Answer 27

displacement of the medium is perpendicular to the direction of travel of the wave

Question 28

longitudinal wave

Answer 28

particle movement is parallel to the motion of the wave itself

Question 29

wave speed equation

Answer 29

v = λf v = wave speed λ = wavelength f = frequency

Question 30

transverse wave function moving in the +x direction

Answer 30

y(x, t) = A cos [ 2π (x/λ - t/T) ] = Acos[kx - ωt) A = amplitude x = position λ = wavelength T = period k = 2π /λ

Question 31

transverse wave fcn moving in the - x direction

Answer 31

y(x,t) = Acos(kx +ωt)

Question 32

transverse velocity

Answer 32

v_y(x,t) = ωAsin(kx - ωt) * it's the derivative of the transverse wave fcn

Question 33

transverse acceleration

Answer 33

a_y(x,t) = -ω^2y(x,t)

Question 34

if the tension is increase what happens to the wave speed?

Answer 34

the wave speed increases

Question 34

transverse impulse is equal to...

Answer 34

transverse momentum

Question 35

wave speed equation

Answer 35

v = sqrt (F/ μ) F = tension in string μ = mass per unit length v = sqrt( restoring force returning system to equilibrium/ inertia resisting return to equilibrium)

Question 36

power for sinusoidal waves

Answer 36

P(x,t) = sqrt(μF)ω^2A^2sin(kx - ωt) μ = mass per unit length F = tension in string ω = wavelength A = amplitude k= force constant x= displacement t= time

Question 36

max value for power occurs at

Answer 36

P_max = sqrt(μF)ω^2A^2

Question 37

average power occurs at

Answer 37

P_av = (1/2)sqrt(μF)ω^2A^2 P_av = average power, sinusoidal wave on a string μ = mass per unit length F = tension in string ω = angular frequency A = wave amplitude

Question 38

Inverse - square law for intensity

Answer 38

I_1/I_2 = r^2_2/r^2_1

Question 39

intensity

Answer 39

the time average rate at which energy is transported by the wave per unit

Question 40

intensity is inversely proportional to...

Answer 40

the squared distance from the source

Question 41

principle of superposition

Answer 41

as two pulse overlap and pass each other, the total displacement of the string is the algebraic sum of the displacement at that point in the individual pulses

Question 42

nodes

Answer 42

points that don't move at all

Question 43

antinodes

Answer 43

midway between nodes where amplitude is greatest

Question 44

destructive interference

Answer 44

happens at nodes where two waves are always equal and opposite therefore they cancel out

Question 45

constructive interference

Answer 45

happens at antinodes, the two waves are identical and result in a larger displacement

Question 46

standing wave on a string, with a fixed end at x =0

Answer 46

y(x,t) = (A_sw*sinkw)sinwt A_sw = standing wave amplitude = 2A k = wave number ω = angular frequency

Question 46

adjacent nodes are one half wavelength apart. whats the equation to find it

Answer 46

λ_n = 2L/n

Question 47

whats the general equation for harmonics ?

Answer 47

f_n = n(v/(2L)) = nf_1 f_n = standing wave frequencies, string fixed at both ends f_1 = fundamental fequency n = 1,2,3,4... v = wave speed L = length of string

Question 48

fundamental frequency equation

Answer 48

f_1 = 1/(2L)sqrt(F/μ) = v/(2L)

Question 49

audible sound range for humans

Answer 49

20-20000 Hz

Question 50

ultrasonic vs. infrasonic

Answer 50

ultra = above audible range infra = below audible range

Question 50

P_max , pressure amplitude of sinusoidal wave fcn

Answer 50

P_max = BkA B = bulk modulus k = wave number = 2π/λ