Waves, Sound and Optics

Question 1

Hooke’s law

Answer 1

F = -kx

large k = stiff, strong spring

Question 2

elastic potential energy

Answer 2

PE(elastic) = 1/2kx^2

Question 3

elastic kinetic energy

Answer 3

KE(elastic) = 1/2mv^2

Question 4

period and frequency relationship

Answer 4

f=1/T T=1/f

Question 5

frequency of a spring

Answer 5

f = 1/2π√k/m

Question 6

period of a spring

Answer 6

T = 2π√m/k

Question 7

restoring force for a pendulum

Answer 7

F(restoring) = mgsinθ

Question 8

frequency for a pendulum

Answer 8

f = 1/2π√g/l

l is length of pendulum, g gravity

Question 9

period for a pendulum

Answer 9

T = 2π√l/g

Question 10

KE and PE for a pendulum

Answer 10

KE = 1/2mv^2
PE = mgh

Question 11

wave equation

Answer 11

v = fλ

Question 12

2 big wave rules

Answer 12

1) same medium, same speed.
2) different medium, same frequency.
* these rules hold for transverse AND longitudinal waves!

Question 13

standing wavelengths for 2 fixed ends, and fundamental wavelengths

Answer 13

λn = 2L/n, λn = λ1/n
n = nodes - 1
L = length of rope
λ1 = fundamental wavelength
*for first (fundamental) harmonic, n =1

Question 14

standing wave frequencies for 2 fixed ends, and fundamental frequencies

Answer 14

fn = nv/2L, fn = n(f1)
n = nodes - 1
L = length of rope
f1 = fundamental frequency

Question 15

describe the speed of sounds through different media

Answer 15

v = solids > liquids > gasses

faster with increased resistance to compression and decreased density

Question 16

standing waves in a tube (both ends open)

Answer 16

λn = 2L/n
fn = nv/2L

Question 17

standing waves in a tube (one end open)

Answer 17

λn = 4L/n
fn = nv/4L
Only odd n!

Question 18

beat frequency

Answer 18

f(beat) = |f1 - f2|

Question 19

Intensity formula

Answer 19

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

Question 20

the doppler effect

Answer 20

fo = fs ( v ± vo / v ± vs )

Question 21

speed of light in a vacuum

Answer 21

c = 3 x 10^8 m/s

Question 22

energy of a photon

Answer 22

E = hf = hc/λ
h = planck's constant

Question 23

energy is proportional to ____ for waves and ____ for particles.

Answer 23

square of amplitude

frequency

Question 24

index of refraction. I.O.R. for air? speed?

Answer 24

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.

Question 25

Snell’s law and implications

Answer 25

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

Question 26

critical angle for total internal reflection

Answer 26

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.

Question 27

Focal length

Answer 27

f = 1/2Rc
Rc = radius of curvature

Question 28

Mirror/Lens equation

Answer 28

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)

Question 29

magnification equation

Answer 29

m = -i/o
same for lenses and mirrors
if m is + upright, - inverted

Question 30

Lens power (also for multiple lenses)

Answer 30

P = 1/f (f must be in meters)

-‘ve and +’ve f still applies

Question 31

myopia and how to correct it

Answer 31

Myopia = nearsightedness, can’t see far, image focused before the retina
fixed with diverging lens

Question 32

hyperopia and how to correct

Answer 32

hyperopia = farsightedness, can’t see near, image focused beyond the retina
fixed with converging lens

Question 33

presbyopia and how to correct

Answer 33

presbyopia = inability to accommodate eye, corrected with converging lens.