Waves, Sound and Optics Flashcards
Hooke’s law
F = -kx
large k = stiff, strong spring
elastic potential energy
PE(elastic) = 1/2kx^2
elastic kinetic energy
KE(elastic) = 1/2mv^2
period and frequency relationship
f=1/T T=1/f
frequency of a spring
f = 1/2π√k/m
period of a spring
T = 2π√m/k
restoring force for a pendulum
F(restoring) = mgsinθ
frequency for a pendulum
f = 1/2π√g/l
l is length of pendulum, g gravity
period for a pendulum
T = 2π√l/g
KE and PE for a pendulum
KE = 1/2mv^2 PE = mgh
wave equation
v = fλ
2 big wave rules
1) same medium, same speed.
2) different medium, same frequency.
* these rules hold for transverse AND longitudinal waves!
standing wavelengths for 2 fixed ends, and fundamental wavelengths
λn = 2L/n, λn = λ1/n n = nodes - 1 L = length of rope λ1 = fundamental wavelength *for first (fundamental) harmonic, n =1
standing wave frequencies for 2 fixed ends, and fundamental frequencies
fn = nv/2L, fn = n(f1) n = nodes - 1 L = length of rope f1 = fundamental frequency
describe the speed of sounds through different media
v = solids > liquids > gasses
faster with increased resistance to compression and decreased density
standing waves in a tube (both ends open)
λn = 2L/n fn = nv/2L
standing waves in a tube (one end open)
λn = 4L/n
fn = nv/4L
Only odd n!
beat frequency
f(beat) = |f1 - f2|
Intensity formula
β = 10log(10)I/Io
measures sound intensity in dB (intensity also measured in W/m^2)
add 10 to β, multiply I by 10
subtract 10 from β, divide I by 10
the doppler effect
fo = fs ( v ± vo / v ± vs )
speed of light in a vacuum
c = 3 x 10^8 m/s
energy of a photon
E = hf = hc/λ h = planck's constant
energy is proportional to ____ for waves and ____ for particles.
square of amplitude
frequency
index of refraction. I.O.R. for air? speed?
index of refraction = speed of light in vacuum/speed of light in medium
n = c/v
use n=1 for air
The greater n, slower speed.
Snell’s law and implications
n1sinθ1 = n2sinθ2
- when second medium has higher n, moves slower and bends towards the normal
- when second medium has lower n, moves faster and bends away from the normal
critical angle for total internal reflection
sinθcrit = n2/n1
If the angle of incidence is greater than θcrit, total internal reflection occurs
Only occurs when going from high n1 to lower n2.
Focal length
f = 1/2Rc Rc = radius of curvature
Mirror/Lens equation
1/f = 1/o + 1/i
o is always positive, i and f vary (+ if on same side as observer for mirror, + if on opposite side for lens) (if i is - virtual, if + real for both lenses and mirrors)
magnification equation
m = -i/o
same for lenses and mirrors
if m is + upright, - inverted
Lens power (also for multiple lenses)
P = 1/f (f must be in meters)
-‘ve and +’ve f still applies
myopia and how to correct it
Myopia = nearsightedness, can’t see far, image focused before the retina
fixed with diverging lens
hyperopia and how to correct
hyperopia = farsightedness, can’t see near, image focused beyond the retina
fixed with converging lens
presbyopia and how to correct
presbyopia = inability to accommodate eye, corrected with converging lens.
