AP Physics
Supplement 1
Waves, Light, & Sound
Waves
T = 1/f
f = 1/T
V = fλ
Sound
Relative Intensity:
dB  10 Log
I
Where I0 = 10 -12 W/m2
I0
Law of Pipes:
Open: λ ≈ 2l or λ = 2(l + 0.8d)
Closed: : λ ≈ 4l or λ = 4(l + 0.4d)
Law of Strings:
Length:
f
l'

f' l
Diameter:
f
d'

f' d
Tension:
f

f'
Density:
f

f'
F
F'
D'
D
Doppler Effect:
Stationary Listener – Moving Source
Source Approaching – Listener in Front (Lf)
v
f lf  f s
v = speed of sound, vs = speed of source
v  vs
Source Moving Away – Listener Behind (Lb)
v
f lb  f s
v = speed of sound, vs = speed of source
v  vs
Stationary Source – Moving Listener
Listener Approaching – Listener Closing (Lc)
v  vlc
v = speed of sound, vlc = speed of listener
f lc  f s
v
Listener Approaching – Listener Opening (Lo)
v  vlo
v = speed of sound, vlo = speed of listener
f lo  f s
v
Light
Light has a dual nature. This means that it exhibits properties of both waves and particles. The
current definition of light is a photon of energy carried by or upon a wave front.
A Photon is a discrete packet of energy. The visible spectrum is the range of wavelengths of
electromagnetic radiation which stimulate the human retina (4 x 10-7 m < λ < 7.5 x 10-7 m).
White light is a combination of all colors of the visible spectrum, while black is the absence of
all colors. White light can be separated into its component colors by diffraction which is the
bending of light. Since light is part of the electromagnetic spectrum, all light has the same speed
(3 x 108 m/s in a vacuum) and since v =fλ, frequency is inversely proportional to wavelength.
Hence colors of light which have the longest wavelength have the lowest frequency and those
with the shortest wavelength have the highest frequency.
The visible spectrum of light, has the following component colors listed from lowest frequency
(longest wavelength) to highest frequency (shortest wavelength)
R O Y
E R E
D A L
N L
G O
E W
G
R
E
E
N
B
L
U
E
I
N
D
I
G
O
V
I
O
L
E
T
Frequencies below the visible spectrum are called infrared and those above the violet are called
ultraviolet.
The instrument used to measure wavelengths of light is called a spectroscope.
Quantum Theory of the atom says that an electron in the electron cloud can only absorb energy
if that energy is enough to move it to the next level in the cloud. This moves the electron from
its normal or ground state to a higher energy or excited state. In order to lose this extra, set
amount of energy, the electron gives off light.
Max Planck found that the color or frequency of light given off corresponded to the amount of
energy given off according to the equation:
E = hf
Where h is a constant = 6.626 x 10-34 J•s and f = the frequency of light given off.
Hence energy is in joules. This atomic spectra or the spectrum of light given off by a specific
electron structure gives rise to the branch of chemistry called spectroscopy which is the
identification of chemical composition by examination of the light a compound gives off.
Law of Reflection – the angle of incidence is equal to the angle of reflection.
Plane Mirrors
 All images are virtual
 Image and Object sizes are the same
 Image and Object Distances are the same
Spherical Mirrors
 Images are either real or virtual
o Real images appear on the same side of the mirror as the object
o Virtual images appear in the mirror (i.e. on the opposite side of the mirror.
 Object distances are always positive
 Image distances are negative if the image is virtual and positive if the image is
real.
 Concave mirrors
o Reflective on the inside
o Have positive focal lengths
 Convex Mirrors
o Reflective on the outside
o Have negative focal lengths
Lenses
 Images are either real or virtual
o Real images appear on the opposite side of the lens as the object
o Virtual images appear on the same side of the lens.
 Object distances are always positive
 Image distances are negative if the image is virtual and positive if the image is
real.
 Lenses are either converging or diverging
o Concave lenses are diverging and have negative focal lengths
o Convex lenses are converging and have positive focal lengths.
Equations
1
1
1


f di do


m
hi
d
 i
ho
do
These work for both mirrors and lenses!
If magnification is positive, image is upright.
If magnification is negative, image is inverted.
For Lenses
1
Power is measured in diopters, focal length must be in meters!
P
f
Refraction
sin i
n
sin r
the n value.
n
C
If you are going out of a substance into air you use the reciprocal of
vs
If you are going from one substance into another you find the n for the boundary by
dividing the n value of what you are going into by the n value of what you are coming out
of.
Primary Colors of Light vs. Primary Pigments
Primary colors of light are Red, Green, and Blue. When all three are combined you get white
light. When they are combined in pairs you get the complement of the third color.
Combination
Produces
Green and Blue Cyan
Red and Blue
Magenta
Green and Red Yellow
Which is the
complement of
Red
Green
Blue
Hence
Red + Cyan = White
Magenta + Green = White
Yellow + Blue = White
Pigments (i.e. inks and paints) are subtractive. This means that each color added causes less
light to be reflected! The primary pigments are Cyan, Yellow, and Blue. If you have ever
looked at a color print cartridge, these are the colors of the inks in the cartridge. If you add the
three primary pigments they produce the color black. Hence they have subtracted out all of the
reflected light. (Remember that black is the absence of reflections or light)
In pairs they produce their complimentary color by subtraction.
Combination
Magenta and Yellow
Magenta and Cyan
Yellow and Cyan
Which are made of
(Red + Blue) + (Green + Red)
(Red + Blue) + (Green + Blue)
(Red + Green) + (Green + Blue)
Produces
Red
Blue
Green
Problems
Intensity
1. Calculate the intensity of the sound waves from an electric guitar’s amplifier at a distance
of 5 m when its power output is equal to each of the following values:
a. 0.25 W
b. 0.50 W
c. 2 W
2. If the intensity of a person’s voice is 4.6 x 10-7 W/m2 at a distance of 2 m, how much
sound power does that person generate?
3. How much power is radiated as sound from a band whose intensity is 1.6 x 10-3 W/m2 at a
distance of 15 m?
4. The power output of a tuba is .35 W. At what distance is the sound intensity of the tuba
1.2 x 10-3 W/m2.
5. When the decibel level of traffic in the street goes from 40 to 60 dB, how much greater is
the intensity of noise?
Pipes and Strings
6. What is the fundamental frequency of a .2 m long organ pipe that is closed at one end,
when the speed of sound in the pipe is 352 m/s?
7. A flute is essentially a pipe open at both ends. The length of the flute is 66 cm. What are
the first three harmonics of a flute when all keys are closed? The speed of sound in the
flute is 340 m/s.
8. What is the fundamental frequency of a guitar string when the speed of waves on the
string is 115 m/s and the effective string lengths are as follows?
a. 70 cm
b. 50 cm
c. 40 cm
9. A violin string that is 50 cm long has a fundamental frequency of 440 Hz. What is the
speed of the waves on this string?
10. If this string is shortened to 30 cm, what is its fundamental frequency?
11. If the tension on the shortened string is tripled, what will be its new fundamental
frequency?
Doppler Effect
12. If the police car with a 365 Hz siren is traveling at 60 mph towards you, on a summer day
of 28 °C, what frequency would you hear?
13. If a fire truck with a 340 Hz siren is traveling at 45 mph away from you, on a cold winter
day of 10 °C, what frequency would you hear?
Refraction
o
o
14.The angle of incidence in water is 67 and the angle of refraction in a second material is 47 .
Determine everything you can about the action at the water/material 2 boundary. Also
determine the index of refraction of the second material. (Recall: The index of refraction for
water is 1.33.)
15.. An underwater flashlight is placed on a swivel so that it can be made to strike the water-air
boundary at different angles. For each incident angle, report the light action at the water-air
boundary.
o
Incident angle = 25
o
Incident angle = 35
o
Incident angle = 45
o
Incident angle = 55
Optics
16. A 2.0-cm object is placed 25.0-cm in front of a converging lens of focal length 20-cm.
Determine everything you can about the size and location of the image.
17.A 3.0-cm object is placed 12.0-cm in front of a converging lens of focal length 15.0-cm.
Determine everything you can about the size and location of the image.
18.A virtual image of height 12-cm is produced 36-cm in front of the lens when a 10.cm object is
placed in front of a converging lens. Determine everything you can about the relationship
between the object and the lens.
19.A 5.0-cm object is placed 12-cm in front of a lens. A virtual image of height 4.0-cm is
produced. Determine everything you can about the image and the lens.