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Physics Day 2
Sound
1. Production of sound- fluctuations in the pressure of a solid, liquid, or gas. Vibrating
objects induce sound by creating changes in pressure within the medium. For instance, in
air a vibrating object will create fluctuations in air pressure that has alternating higher and
lower pressure. These fluctuations cause our eardrums to vibrate with the same
frequency.
2. Relative speed of sound in solids, liquids and gases. Remember that sound involves
molecules hitting other molecules in the propagation of the wave, thus the closer together
the molecules the faster the wave can travel. In general: the speed of sound is
gas<liquid<solid. Think about how both temperature and the composition of the medium
will affect the speed of sound.
For example: Air at 0oC vs. at 20oC and pure water vs. sea water
The speed of an object relative to the speed of sound can be described as subsonic, sonic,
and supersonic. Supersonic speeds are often described in terms of mach number.
Mach number = speed of object/speed of sound
3. Intensity of sound- rate at which a wave of any kind carries energy per unit crosssectional area (of a sphere): I = P/(4r2). A decibel is the unit for measuring the intensity
of sound: = 10 log I/Io (*memorize*) where I is the intensity of the sound and Io is the
threshold intensity. The sound intensity is inversely proportional to the distance squared
from the source: I1/I2 = r22/r12 thus you can see the change in sound intensity from a
change in the distance.
#1. The intensity level of Sound B is 20 dB greater than the intensity level of
Sound A. How many times greater is the intensity level of Sound B than
the intensity level of Sound A?
A. 2
B. 10
C. 20
D. 100
Problem 12.10 and 12.12
4. Attenuation
5. Doppler effect- a change in the frequency of a wave (either sound or light) brought about
by relative motion between the source and the observer. Think in general terms for a
moving sound source or observer.
Problems 12.8 and 12.9
6. Pitch- refers to frequency changes in the sound.
7. Resonance in pipes and strings already discussed during day 1
8. Harmonics- already discussed on day 1.
9. Ultrasound- sounds whose frequencies are above 20,000 Hz
Passages #1 and #3
Fluids and Solids
A. Fluids
1. Density is a property of all fluids. Density is a measure of how tightly molecules are
packed together. For example, solids tend to have a higher density than liquid because
the molecules composing the solid are more tightly packed. Specific gravity is a measure
of the density of some substance as compared to the density of pure water. For example,
water has a specific gravity of 1 where as something such as lead will have a higher
specific gravity because its density is higher compared to water.
2. Buoyancy, Archimededs’ principal
Buoyancy is the upward force acting on an object in a fluid.
Archimedes’ principle is FB = Vg where V is the volume,  is the density and g is gravity.
The buoyant force on an object in a fluid is equal to the weight of the fluid the object
displaces. Archimedes’ principle holds whether the object floats or sinks. If the object’s
weight is greater than the buoyant force, it sinks. If its weight is less than the buoyant force,
it floats, in which case the volume V refers only to the submerged part.
Problem 10.5
3. Hydrostatic pressure- the pressure that water exerts. It is a component of the total
pressure of a system.
a. Pascal’s law states that an external pressure exerted on a fluid is transmitted
uniformly throughout the volume of the fluid.
b. P = gh (pressure vs. depth)
4. Viscosity- it is the internal friction in a fluid. Viscosity is inversely proportional to the
temperature of liquids (increase T leads to decrease viscosity) but directly proportional to
the temperature of gases within a fixed volume (increase T leads to increase in viscosity).
A practical example is a patient who is hypothermic. Their decrease in core body
temperature leads to increased viscosity of their blood, which impedes its flow and may
lead to a stroke or heart attack.
Poiseuille flow
5. Continuity equation describes the flow of a fluid through a pipe
Flow rate (R) = vA (*memorize*) where v is the velocity of the fluid and A is the crosssectional area of the pipe. If the A changes within a single system then you can have
v1A1 = v2A2
Problem 10.7
6. Concept of turbulence at high velocities- cigarette smoke, the foot of a waterfall.
7. Surface tension- a liquid surface is like a membrane under tension. It is the tendency of a
liquid drop to assume a spherical shape. The higher the surface tension of the liquid, the
more it wants to form a sphere in a resting drop. In general, as the temperature increases,
the surface tension decreases. Only mercury has a higher surface tension than water.
Concepts of cohesion vs. adhesion: cohesion is the force keeping like molecules together
and adhesion is the force keeping different molecules together.
8. Bernoulli’s equation- relates pressure, speed, and height of a moving liquid. The units
are pascals (Pa) where 1 atm = 105 Pa.
P1 + gh1 + (1/2)v12 = P2 + gh2 + (1/2)v22 where P is the pressure. This equation
assumes that the liquid is incompressible and that the viscosity is negligible.
Problem 10.9
For a liquid at rest: P2 – P1 = g(h1 – h2) here, you can compare the change in pressure
from one depth to another within a liquid.
Torricelli’s equation: v = (2gh)1/2 (*memorize*). This equation is useful if you have a
container filled with some liquid and you puncture the container at the bottom and you
need to determine how fast the liquid is coming out.
Problems 10.10 and 10.11
Passages #12 and #8
B. Solids are mostly crystalline where the atoms are arranged in a regular pattern but can be
amorphous where there is no regular pattern of the atoms making up the solid.
1. Density- already discussed
2. Elastic Properties (elementary properties) are demonstrated by all solids.
Young’s Modulus (= (F/A)/(L/Lo) = stress/strain where F is the force applied, A is
the cross-sectional area, L is the change in length and Lo is the original length. In
general, a thick solid stretches less than a thin one and a long solid will stretch more than
a short one under a given force. Each solid will have its own unique Young’s Modulus
#2. Two copper wires have the same length but different diameters. The
diameter of Wire A is 2 times the diameter of Wire B. If identical weights
are suspended from these wires, what is the ratio of the change in length of
Wire A to the change in length of Wire B?
A.
B.
C.
D.
1:4
1:2
1:1
2:1
Problems 9.3 and 9.4
3. Elastic limit is the amount by which a solid can distort without being permanently
altered.
4. Thermal expansion coefficient is a constant whose value depends on the nature of the
material. L = (a)(Lo)(T), a long steel bridge may vary in length by over a meter
between summer and winter.
5. Shear is a measure of rigidity
Shear modulus (S) = (F/A)/(s/d) = stress/strain where s is the amount of displacement
and d is the distance between the block faces.
Problem 9.5
6. Compression is a measure of the “squeezablity” of a solid
Bulk Modulus (B) = -(F/A)/(V/Vo) = stress/strain where V is the change in volume
and Vo is the original volume. Remember that P = F/A where P is the pressure.
Electrostatics and Electromagnetism
A. Electrostatics
1. Charge-comes from protons and electrons. Conductors- are materials that allow charge
to flow easily through. Charge conservation maintains that the net electric charge in an
isolated system remains constant (either neutral, positive, or negative)
2. Insulators- are materials that impede the flow of charges
3. Coulomb’s law- the force between 2 electric charges also called electric force: F =
kq1q2/r2 (*memorize*), where q is the charge on a particle. It was this equation that gave
rise to the law of gravitation.
The charge on an electron is 1.6 x 10-19 C (*memorize*)
#3. Two charged particles are a distance r apart. If the charges on the 2
particles and the distance between the particles are doubled, how does the
force between the particles change?
A. It decreases by a factor of 2
B. It stays the same
C. It increases by a factor of 2
D. It increases by a factor of 8
Problem 16.1
4. Electric fields lead to a force on the charge where E = F/q
Problem 16.4
a. Field lines- imaginary lines that help us picture an electric field. The lines leave the
positive charges and enter the negative charges. Close lines indicates that the
field is strong and vice versa.
b. The field will vary due to differences in charge distribution in an asymmetric object.
5. Potential difference- is the work that must be done to take charge q from one point to
another: V = W/q = Ed, where d is the distance between the charges. Remember, KE =
W = qV = 1/2mv2 to relate electricity and translational motion.
6. Equipotential lines- all points on these lines are at the same voltage. They can be drawn
at any point in the field
7. Electric dipole
a. Definition of dipole- created by two opposite charges with equal magnitude.
b. Behavior in electric field- the dipole will tend to align itself along the field in the
opposite orientation to the field.
c. Potential due to dipole
8. Electrostatic induction
9. Gauss’ law –involve charges at the surface
B. Magnetism
1. Definition of the magnetic field (B) = F/(qv sin ) (*memorize*)
2. Existence and direction of force on charge moving in magnetic field, think of the right
hand rule.
3. Orbits of charged particles moving in magnetic field
4. General concepts of sources of magnetic field
5. Nature of solenoid (a coil of wire in the form of a helix) is the same as the magnetic field
of a bar magnet. A toroid is a solenoid bent into the shape of a donut.
6. Ampere’s law for magnetic field induced by current in straight wire and other simple
configurations
7. Comparison of E and B relations
a. Force of B on a current
b. energy
C. Light, electromagnetic radiation
1. Properties of electromagnetic radiation- requires no material medium for travel, every
object emits EM waves, the hotter the object the faster it radiates energy, ability to emit EM
waves is proportional to the ability to absorb it.
a. velocity equals constant c ( 3 x 108 m/s), in a vacuum
b. electromagnetic radiation consists of perpendicularly oscillating electric and
magnetic fields; direction of propagation is perpendicular to both
2. Classification of electromagnetic spectrum. (longest wavelength) Radio, microwaves,
infrared, ROYGBIV (visible spectrum), ultraviolet, x-ray, gamma ray (shortest
wavelength)
Electronic Circuit Elements
A. Circuit elements
1. Current I = Q/t, the units are Ampere (A) = C/s
2. Electromotive force- the potential difference of a source, such as a battery, not connected
to any external circuit.
3. Internal resistance of battery- all batteries will have an internal resistance that will
decrease the effective voltage, called the Ir drop (i.e., a 9V battery will actually produce a
voltage somewhat less than 9V due to internal resistance): V =  - Ir, where is the
electromotive force and r is the internal resistance of the battery.
Problem 18.15
4. Resistance
a. Ohm’s law; I = V/R (*memorize*)
b. Resistors in series: RT = R1 + R2 + … Rn. (*memorize*). Here, current is
constant the entire time and the voltage changes. The equivalence resistance is
greater than any one resistor.
Problem 18.9 a, b, and c
c. Resistors in parallel: RT = (R1R2Rn)/(R1 + R2 +… Rn). (*memorize*). Here,
voltage is constant and the current changes. The equivalence resistance is
smaller than any one resistor.
#4. A 12-V battery causes a current to flow through a circuit consisting of a
24-o and an 8-o resistor in parallel. What current flows through the 8-o
resistor?
A. 0.5 A
B. 1.0 A
C. 1.5 A
D. 2.0 A
Problem 18.11 a and b
d. Resistivity ( = RA/L)- is the ability of a substance to conduct current thus it is a
property of the material only. R is the resistance, A is the cross-sectional area of
the wire, and L is the length of the wire.
The longer the conductor, the greater its resistance. The thicker the conductor,
the less its resistance.
Problem 18.13
Passage #II
5. Capacitance (C) = q/V. Units are in Farads (F) = C/V
a. Concept of parallel plate capacitor- a pair of conductors that store energy in the
form of an electric field.
b. Energy of charged capacitor (W) = 1/2qV. The capacitance decreases when the
distance between capacitors increases and vice versa. Also, the capacitance
decreases when the area of each capacitor decreases and vice versa. Thus C 
A/d.
Problem 17.8
c. Capacitors in series (the same as resistors in parallel): CT = (C1C2Cn)/(C1 + C2
+… Cn). (*memorize*). Current is constant and voltage changes.
Problem 17.11
d. Capacitors in parallel (the same as resistors in series): CT = C1 + C2 + … Cn
(*memorize*). Current changes and voltage is constant.
Problem 17.12
e. Dielectric- putting an insulator between capacitor plates decreases the voltage
across the charged capacitor. Materials have different dielectric strengths.
6. Discharge of a capacitor through a resistor
B. Circuits
Power in circuits: P = IV, P = I2R (*memorize*)
Problems 18.6 and 18.8
C. Alternating currents and reactive circuits
1. root-mean-square current
2. root-mean-square-voltage
Passage #6
Light and Geometrical Optics
A. Light, electromagnetic radiation
1. Concept of interference; Young double slit experiment
2. Thin films, diffraction grating, single slit diffraction
3. Other diffraction phenomena, x-ray diffraction
4. Polarization of light- vibrations occur in only one direction (true for only transverse
waves…longitudinal waves cannot be polarized).
Light can be polarized when reflected off of some surface at a particular angle: tan p =
n2/n1 where p is the angle of incidence of the light, n is the index of refraction of the
medium.
Problem 24.7
5. Visual spectrum- already discussed above. How does color appear?
a. Energy is directly proportional to the frequency of the wave.
b. Lasers can be tuned to emit a single wavelength of light.
B. Geometrical Optics
1. Reflection from plane surface: angle of incidence equals angle of reflection. Diffuse vs.
specular reflection.
2. Refraction- already discussed above. Refractive index (n)- is a ratio of speed of light in
free space and its speed in some medium: n = c/v.
Snell’s law: n1 sin i = n2 sin r where i is the incident wave and r is the reflected wave
Problems 22.3 and 22.4
3. Dispersion- occurs to a beam containing more than 1 wavelength. The beam splits into a
corresponding number of different beams when it is refracted. For example, a prism
creates a spectrum of colors from white light. Also, think of how a rainbow forms. The
wavelength of light dictates how much the light will refract. In general, the higher the
frequency of the light, the more it will bend.
4. Total internal reflection- occurs when the angle of incidence is equal to the critical angle:
sin ic = n2/n1
Passage IV
5. Spherical mirrors
a. Center of curvature is equal to the radius of the circle.
b. Focal length is the center of curvature divided by 2.
c. Real and virtual images depend on the where the image appears relative to the
object. Real images appear on the same side of the mirror as the object and
virtual images appear on the opposite side as the object.
d. The characteristics of the image (real vs. virtual, erect vs. inverted, size)
correspond to the location of the object with respect to the focal point and the
center of curvature.
Concave Mirror
Object Position
between mirror and f
at f
between f and c
at c
beyond c
Image Characteristics
virtual, erect, larger than object
no image
real, inverted, larger than object
real, inverted, same size as object
real, inverted, smaller than object
Convex Mirror
Object Position
anywhere
Image Characteristics
virtual, erect, smaller than the object
#5. A concave spherical mirror has a radius of curvature of 50 cm. At what
distance from the surface of this mirror should an object be placed to form
a real, inverted image the same size as the object?
A. 20 cm
B. 30 cm
C. 50 cm
D. 100 cm
6. Thin lenses
a. Converging and diverging lenses
b. Use of formula 1/p + 1/q = 1/f (*memorize*), where p is the distance of the
object from the lens, q is the distance of the image from the lens, and f is the
focal length. The sign of the variables depends on the location relative to the
lens.
c. Lens strength: dipoters (D) = 1/f is used for corrective lenses. Nearsighted
(myopia) vs. Farsighted (hyperopia). In the former, light coming into the eye
from an object at a distance comes into focus in front of the retina. In the latter,
light coming into the eye from an object nearby comes into focus behind the
retina. Essentially, a nearsighted person can read a book fine but not street signs
and the vice versa is true for a farsighted person.
d. The size or magnification of an image can be calculated m = q/p = n2/n1 = h’/h
where q is the size of the image, p is the size of the object, n2 is the index of
refraction of the medium the object is in, n1 is the index of refraction of the
medium the viewer is in, h’ is the apparent depth and h is the actual depth.
e. The characteristics of the image (real vs. virtual, erect vs. inverted, size)
correspond to the location of the object with respect to the focal point and the
center of curvature and are the exact same for mirrors.
Converging Lens
Object Position
between mirror and f
at f
between f and c
at c
beyond c
Image Characteristics
virtual, erect, larger than object
no image
real, inverted, larger than object
real, inverted, same size as object
real, inverted, smaller than object
Diverging Lens
Object Position
anywhere
Image Characteristics
virtual, erect, smaller than the object
Problem 23.8
7. Combination of lenses is used to minimize the various aberrations discussed below.
8. Lens aberration- means that lenses do not give rise to perfect images. For instance, the
image may be of a different color on the fringes because of differences in the index of
refraction (chromatic aberration), and the image may be distorted due to the lens
curvature (spherical aberration).
9. Ray tracing - is not of very much importance on the MCAT
10. Optical instruments
Passage 4
Atomic and Nuclear Structure
A. Atomic Structure and Spectra
1. Emission spectrum of hydrogen (Bohr model)
2. Atomic energy levels
a. Quantized energy levels for electrons
b. Calculation of energy emitted or absorbed when an electron changes energy
levels
Problem 27.1
Passage I
B. Atomic Nucleus
1. Atomic number- the number of protons in a neutral atom. Atomic weight- the weight of
one atom.
2. Neutrons- uncharged nuclear particles, the larger the nucleus, the greater the proportion
of neutrons. Protons- positively charged nuclear particles. Isotopes- are elements of one
type that differ in the number of neutrons in their nuclei. The atomic mass increases with
an increase in the number of neutrons. Isotopes can vary in their physical properties such
as freezing pt, boiling pt, density, etc.
3. Nuclear forces
4. Radioactive decay: alpha- release of a helium atom, occurs when the nucleus is too big.
Beta- two types, positron and electron are emitted, occurs to adjust the proton to neutron
ratio. Gamma- releases a gamma particle, occurs when the nucleus has too much energy.
Half-life- the time required for half of the original sample to decay.
Passage VI
Problem 29.2 and 29.4
exponential decay, semi-log plots
5. General nature of fission: divide and conquer
6. General nature of fusion: how the sun and stars get their energy, requires high
temperature and high density
7. Mass deficit is a phenomenon found when measuring the mass of an atom and comparing
it to the total mass of its parts. This loss of mass can be plugged into the E = mc2
equation to determine the amount of energy holding the nuclear components together.