Physics Review 7
Name __________________________
Formula
Mechanical wave
Symbol and Units
Formula
do > +f
do < +f
Symbol and Units
–f
A
 amplitude, A: maximum height measured from the midpoint (m)
 wavelength, : distance between identical points (m)
 frequency, f: the number of waves per unit time (Hz or s-1)
 period, T: the time it takes for one wave to pass (s)
 T = 1/f
 velocity, vw: speed of the waveform, vw = /T = f (m/s)
 transverse wave (string): disturbance  wave 
 longitudinal wave (sound): disturbance  wave 
Interference
 amplitudes combine (superposition principle)
 constructive interference when amplitudes are added
 destructive interference when amplitudes are subtracted
 beats, fbeats = |fA – fB|
vw = velocity of wave in m/s
Velocity of a wave on a string
Ft = force of tension in N
½
vw = (Ft/)
 = linear density in kg/m
Harmonics

n = 2L/n
fn = nf1
Doppler effect
f’ = f(vw ± vo)/(vw ± vs)
approaching: f' > f (+vo, –vs)
receding: f' < f (–vo, +vs)
approximation formula
f/f  v/vw
approaching: f’ = f + f
receding: f’ = f – f
Angle of reflection
i = incoming ray  to surface
i = r
r = reflected ray  to surface
phase shift when ni < nr
n = index of refraction
c = 3 x 108 m/s
Wave velocity in a vacuum
f = frequency of wave in s-1 (Hz)
c = f
 = wavelength in m
Refraction within a medium
n = index of refraction (no units)
vn = c/n
vn = velocity at n in m/s
fn = f1
n = 1/n
Angle of refraction (Snell's law) ni = source medium n
nisini = nRsinR
i = incident angle  to surface
ni < nR: bend toward normal
nR = refracting medium n
ni > nR: bend away from normal R = refracted angle  to surface
 n  to f  color separation = dispersion (prism)
 total reflection when ni > nR and i  c = nlow/nhigh
r = radius of curvature in m
Parabolic mirror radius of
curvature
r = 2f
f = focal length in m
do = object distance to l/m in m
lens/mirror equation
di = image distance to l/m in m
1/do + 1/di = 1/±f
f = focal length in m
+di for real image (-di virtual)
+f for converging (-f diverging) M = magnification (no units)
hi = height of image in m
magnification equation
ho = height of object in m
M = hi/ho = -di/do
F
F
F
F
F
F
F
F
F
F
W = 2L/d'
 = angle from slits to band in m
x = center to band distance in m
L = slits to screen distance in m
m = band order (no units)
 = wavelength of light in m
d = distance between slits in m
W = width of light spot
d' = width of slit
Thickness of a film, T (f = 1/n)
ni < nf < n r
Interference
Bright
T = ½f
Dark
T = ¼f
nf > ni and nr
T = ¼f
T = ½f
Practice Free Response
The following standing wave is generated on a 0.50 m guitar
string.
a.
b.
c.
 = wavelength in m
L = length of string in m
n = number of harmonic
f = frequency
f' = perceived frequency in s-1
f = generated frequency in s-1
vw = wave velocity in m/s
vo = observer velocity in m/s
vs = source velocity in m/s
F
Interference with two slits
tan = x/L
sinc = m/d
sind = (m + ½)/d
c for bright band (d for dark)
Interference with one slit
1.
Determining nth harmonic
F
2.
What is the standing wave's harmonic number?
What is the wavelength?
The string tension is 500 N and the string's mass is
0.055 kg. What is the wave velocity?
d. What is the wave frequency?
e. What is the frequency and wavelength of the first
harmonic?
Two first-order spectral lines, A and B, for helium are
projected onto a meter stick that is 0.50 m from a 600
lines/nm diffraction grating. The wavelengths are 436 nm and
578 nm.
A B
B A
meter stick
0.50 m
Helium discharge tube
Which spectral line is 436 nm and which is 578 nm?
What are the angular deflections of lines A and B?
What is the distance between the ruler's center and lines
A and B?
Given the following arrangement of lens (f = +10 cm) and
object (do = 25 cm), answer the following questions.
a.
b.
c.
3.
a. Draw two rays, which show the position of the image.
b. Circle the three correct descriptions of the image.
real virtual inverted upright larger same size smaller
c. Calculate di and the magnification, M.