Asian Power Systems Review Center
APPLIED PHYSICS
I. THEORIES AND PRINCIPLES
A. Wave Motion and Sound Waves
Wave – is a periodic disturbance. These are produced in all forms of matter and even in empty
space where ordinary matter does not exist.
crest
Wavelength (λ)
Amplitude
v
trough
Types of Waves in Matter:
1. Transverse wave – a wave in which the vibration direction is perpendicular to the
direction of the wave propagation. Examples are water waves, waves in strings under
tension, electromagnetic waves – light and radio waves.
2. Longitudinal (or Compressional) wave – a wave in which the vibration direction is
parallel to the direction of the wave propagation. Examples are sound waves, waves in
rods and in vibrating helical spring.
Wave Terminologies:
1. Period of vibration (T) – is the time taken for a particle to move through a complete
cycle.
2. Frequency of vibration (f) – the number of such vibrations executed by the particle each
second.
3. Crest – the top points on the wave.
4. Trough – the bottom points on the wave.
5. Amplitude (A) – the maximum displacement from their normal position of the particles
that oscillate back and forth.
6. Wavelength (λ) – is the distance between two successive points in a wave.
7. Standing wave – a stationary wave pattern formed in a medium when two sets of
identical wave pass through the medium in opposite directions.
Wave Properties:
1. Reflection – the property of wave which occurs when a wave strike an object or comes
to a boundary or another medium and is at least diverted back into the original medium.
2. Refraction – the wave property which occurs when a wave crosses a boundary into
another medium its speed generally changes because the new material has a different
characteristic. Entering the medium obliquely (at an angle), the transmitted wave moves
in a direction different from that of the incident wave.
3. Diffraction – the property of wave to bend around an edge of an object but is unrelated
to refraction.
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4.
5.
Dispersion – the property of a wave whereby waves of different frequency spread apart
from each other.
Interference – the wave phenomena that occur when two or more waves overlap in the
same region of space.
Wave Equations:
1. The velocity of the wave
V = λf
Where: V is the velocity in m/sec
λ is the wavelength in m
f is the frequency in Hz
2. The Period (T) – is the reciprocal of the frequency.
T=
1
f
Where: T is the period in seconds
3. The Velocity of the Longitudinal Waves in Solids and Liquids
V =
E
ρ
Where: E is the modulus of elasticity in Pascal
ρ is the density in kg/m
4. The Velocity of the Longitudinal Waves in Gases
V = kRT
Where: R is gas constant in KJ/kg
R=
R
And R = 8.314 J-mol/K
MW
MW is the molecular weight in kg/mol
k is a constant
k = Cp / Cv = 1.4 → for air, oxygen and nitrogen
T is absolute temperature in K
5. The Velocity of the Transverse Waves on Stretched Spring or Wire
V=
T
ρ linear
Where: T is the tension in N
ρlinear = mass/length; it is the linear density in N/m
Laws of Vibrating String Under Tension
String under tension at a certain vibration frequency will resonate. Meaning it will vibrate
with large amplitude in vibration patterns. These similar vibration patterns are called standing
waves.
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If the string has n segments long, then
1 
V 
L = n λ  And f n = n 
2 
 2L 
Where: n is the number of segments
fn is the frequency of n segments
L is the length of the string
V is the velocity
Fundamental Frequency – is the lowest natural frequency.
fT =
V
Where: n = 1 → fundamental frequency
2L
All the other natural frequencies are integral multiple of the fundamental frequency
V  n
f n = n  =
 2L  2L
T
ρ linear
= nf 1
(For n = 1, 2, 3 …)
The set of frequencies: f1, f2 = 2f1, f3 = 3f1 … are called harmonic series.
B. The Nature of Sound
Sound – is a disturbance or vibration whose energy must be communicated into a medium.
Classification of sound waves:
1. Music – a sound of one regular vibration or more definite frequencies.
2. Noise – a sound of irregular vibration or of no definite range of frequency.
Three physiological characteristics of sound:
1. Pitch – is the highness or lowness of a note or tone.
2. Intensity – is also known as the “loudness” of sound. It is the rate at which sound energy
flows through a unit area.
3. Quality – also known as timbre in which depends on the waveform or vibration from the
source.
Sound Terminologies:
1. Echo – is the reflected sound.
2. Reverberation – the successive echoes that can be heard.
3. Audible Range – the hearing range of human being between 10 Hz to 20,000 Hz.
4. Ultrasonic – sound that has a frequency too high to be heard by human ear, above 20,000
Hz.
5. Infrasonic – sound that has a frequency too low to be heard by human ear, below 20 Hz.
6. Shock Wave – the cone-shaped wave made by an object moving at supersonic speed
through a fluid.
7. Sonic Boom – is the loud sound resulting from the incidence of a shock wave.
8. Rarefaction – rarefied region, or region of lessened pressure, of the medium through
which a longitudinal wave travels.
9. Beats – the alternations of maximum and minimum sound intensity produced by
superposition of two sound waves of slightly different frequencies.
10. Resonance – is the response of a body when a forcing frequency matches its natural
frequency.
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11. Natural frequency – a frequency at which an elastic object naturally tends to vibrate if it
is disturbed and the disturbing force is removed.
Equations:
1. The Relative Sound Intensity. The relative unit of intensity level usually used (in
acoustics) is Bel which can be expressed as:
 I 
B = log10  
 Io 
or
 I 
dB = log10  
 Io 
Where: I is any intensity
Io is the zero level intensity. The smallest intensity for hearing
Io = 1 x 10-16 Watt/cm2
dB is the unit called decibel (dB = 1/10 bel)
2.
The Absolute Sound Intensity. The absolute intensity of sound is proportional to the
square of the pressure amplitude of the wave and can be expressed as:
I=
P2
2Vρ
Where: P is the pressure amplitude in Pascal
ρ is the density of air (kg/m3)
V is the velocity of sound in air in m/s
I is the intensity (W/cm2)
Doppler Effect
Doppler Effect – is the variation of pitch heard from a moving source of sound.
Three cases considered in connection with Doppler Effect:
1. The source is in motion and the observer is at rest
fL
V
=
fs V ± Vs
Where: fL is the frequency observed by the listener
fs is the frequency produced by the source
V is the velocity of sound in the transmitting medium
Vs is the velocity of the source
Note:
(+) → when the source moves away from the observer
(–) → when the source moves toward the observer
2. The source is at rest and the observer is in motion
f L V ± VL
=
fs
V
Where: VL is the velocity of the listener
Note:
(+) → when the listener moves away from the observer
(–) → when the listener moves toward the observer
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3. Both the observer and the source are in motion
f L V ± VL
=
fs V m Vs
Note:
+VL when listener moves toward the source
–VL when listener moves away from the source
+Vs when source moves toward the source
–Vs when source moves away from the source
C. The Nature of Light
Light – is a form of electromagnetic waves whereby the eye is sensitive. It forms the part of
electromagnetic spectrum from 740 nm (red light) to 400 nm (blue light).
Three theories concerning the nature of light:
1. The Corpuscular (Particle) Theory. In this theory proposed by Newton, a luminous
body was believed to emit particles of light called corpuscles.
2. The Wave Theory. In this theory, Maxwell proposed that light is an electromagnetic
waves.
3. The Wave-Particle Theory. This theory explains the dual property of light as a wave
and at the same time streams of particles or corpuscles.
Laws of Reflection and Refraction
Refraction – is the bending of light around the edge of an object or spreading of light in an
arc after passing through any tiny opening.
Incident ray
Normal
Law of Reflection:
The angle of incidence is equal to the angle of reflection for all wavelengths.
Reflected ray
θi θr
θi = θr
Where: θi is the angle of incidence
θr is the angle of reflection
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Law of Refraction or Snell’s Law:
The ratio of the sine of the angle of incidence to the sine of the angle of reflection is
equal to the inverse ratio of the indexes of refraction.
Incident ray
Reflected ray
θa θr
θb
Refracted ray
sin θ a nb
=
sin θ b n a
Where: na is the index of refraction of medium a
nb is the index of refraction of medium b
Index of refraction, n – is the ratio of the speed of light “c” in vacuum to the speed of
the light in the material
n=
c
v
The wavelength of light in a medium
Light ray changes when it passes from one material to another different index of
refraction.
λ=
λo
n
Where: λ is the wavelength of light in vacuum
λo is the wavelength of light as it passes through a medium
n is the index of refraction of any material. The greater the index of
refraction of a medium the greater the deflection of light beam.
The Critical Angle and Total Internal Reflection
Total Internal Reflection – is a phenomenon wherein the light will be reflected back from the
surface area when the incident angle is greater than the critical angle.
The critical angle for total internal reflection:
sin θ critical =
Note:
nb
na
Total internal reflection occurs when the angle of refraction of a light ray going
from one medium to another pf lower index of refraction equals or exceeds 90°.
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Dispersion – is the splitting up of beam of light which contains several frequencies on passing it t
through a substance whose refracted index changes with frequency.
Polarization – the process of filtering light such that only one, two or definite direction(s) is/are
permitted to pass through a polarizer.
Polaroid – are made of long chains of hydrocarbon molecules that are aligned in a film.
Processes of Polarizing Light:
1. Selective Absorption – is the process that takes place in certain crystals when light in
one plane is transmitted as all the other planes is absorbed.
2. Reflection. Reflected light with an angle of incidence between 1° and 89° is partially
polarized as waves parallel to the reflecting surfaces are reflected more than the other
waves.
3. Scattering – it occurs when light is absorbed and reradiated by particles about the size of
gas molecule that makes up the air.
Malus’s Law
The intensity of light that passed through the polarizer is equal to the product of the
maximum intensity and the square of the cosine of the polarizing angle.
I = I o cos 2 θ
Where: Io is the maximum intensity of light transmitted
I is the intensity transmitted at an angle of θ
θ is the polarizing angle
θ = 0° or 180° (maximum)
θ = 90° or 270° (minimum)
Brewster’s Law (Polarization through Reflection)
If the angle of incidence is equal to the polarizing angle, then the angle of reflected ray is
perpendicular to the reflecting ray.
tan θ p =
nb
na
Where: θp is the polarizing angle
Huygens’s Principle (Propagation of Waves)
Every point on a wave front can be considered as a source of secondary wavelets that
spread out in all directions with the wave speed of the medium. The wave front at any time is the
envelope of these wavelets.
D. Lenses
Lens – is a piece of glass or other transparent materials so shaped that it can produced an image
by refracting light that comes from an object.
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Types of Lenses:
1. Converging lens – a lens that brings parallel light into a single real focal point.
2. Diverging lens – a lens that deviate parallel light outward as through it originated at a
single virtual focal point.
Types of Diverging and Converging Lenses
Thin Lens – is one whose thickness is small compared with the radii of curvature R1 and R2.
The Lensmaker’s Equation – the equation used to obtain the focal length of thin lenses.
 1
1
1 

= (n − 1) +
f
 R1 R2 
Where: n is the index of refraction
f = is the focal length of lens
R1 and R2 are the radii of the curvature
R = (+) if the surface is convex (curved outward)
R = (–) if the surface is concave (curved inward)
R → ∞ for plane lens (1/R = 0)
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Note:
If f = (+) → converging lens
If f = (–) → diverging lens
The Thin Lens Equation – is a simple equation that relates the positions of the image and the
object of a thin lens to the lens’s focal length.
1 1 1
+ =
p q f
Where: p is the distance of object from lens
q is the distance of image from lens
f = is the focal length of lens
Note:
If p = (+) → for real object
If f = (–) → for virtual object
Linear Magnification (m) – is the ratio between the size of the image and of the object.
m=
hi
ho
Where: hi is the image height
ho is the object height
m = (+) if the image is erect
m = (–) if the image is inverted
E. Theory of Relativity
Special Theory of Relativity – proposed by Albert Einstein which is concern with bodies that
are moving with constant velocity.
Postulates of Theory of Relativity:
1. Postulate I. (Principle of Relativity). The laws of physics are the same in all inertia
frame of reference, thus all motion is relative. Velocities of object can only be given
relative to some other objects and is impossible to determine the absolute velocity of the
object.
Note:
The frame of reference is a coordinate system relative to which physical measurements
are taken. It moves with constant velocity or the one that is not accelerating.
2. Postulate II. (Principle of Constancy of the Speed of Light). The accurately measured
speed of light in vacuum (c) has the same value for all observers, independent of the
motion of the source or motion of the observer.
Based on these postulates, the following can be predicted:
• Relativistic Mass: The moving body increases its mass, where any change in mass is
equivalent to a change in kinetic energy.
m=
mo
V 
1−  
c
2
Where: m is the relativistic mass
mo is the rest mass
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V is the velocity of the object
c is the speed of the light (c = 3 x 108 m/s)
No object that can be accelerated to the speed of light
•
Linear momentum of a particle when it moves the speed of v
p=
moV
2
V 
1−  
c
•
Time Dilation: Moving clocks are observed to run more slowly than clocks at rest in the
observer’s own frame of reference.
t=
to
V 
1−  
c
2
Where: t is the moving clock
to is the time of the stationary clock (or the observer’s frame of reference)
•
Length Contraction: The length of an object is longest for the observer at rest with
respect to the object and shorter for observers in motion with respect to it (in the direction
of the relative motion of two observers).
L=
Lo
V 
1−  
c
2
Where: L is the realistic length
Lo is the length at rest (or sometimes called as “proper length”)
•
Relativistic Velocity of two Bodies: Suppose a spacecraft (A) is moving with a velocity
VA relative to the earth and a rocket from that spacecraft is fired (in the same direction) at
velocity VB. Then the velocity of the rocket is measured by an observer on the earth is:
V =
V A + VB
V V 
1+  A2 B 
 c 
→ same direction
Where: VA is the velocity of one body
VB is the velocity of the other body (same direction as VA)
V is the relativistic velocity measured by the observer in the earth
•
Relativistic Energy. It is the sum of the kinetic energy and the rest energy.
E = K + mc 2 =
mo c 2
V 
1−  
c
2
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•
Mass-Energy Conversion: A particle moving with the speed approaching the speed of
light possess’ energy
E = mc 2
Where: m is the relativistic mass of the body
mo is the rest mass
v is the velocity of the body
c is the speed of the light
F. Quantum Physics
Quantum – is defined as packets of energy.
Quanta of Radiation: When electromagnetic radiation interacts with atoms and molecules, the
beams acts like streams of energy corpuscles called photons or light quantum
The energy in each photon (E):
E = hf
Where: h is Planck’s constant = 6.626 x 10-34 J-sec
F is the frequency
Note:
c = λf
Photoelectric Effect: When light (particularly ultraviolet light) falls on a metal surface, electrons
are found to be given off. The electrons ejected from the irradiated metal plate are called
photoelectrons.
Einstein Photoelectric Equation – this equation is used to find the maximum kinetic energy of
photoelectrons
Photon Energy = KE max + Wmin Or hf =
1
mV 2 + hf o
2
Where: hfo is the threshold energy (also known as work function)
Wmin = hfo → this is the minimum amount of energy required to pull an electron
from then metal surface
II. REVIEW PROBLEMS
1. The wavelength of a sound wave in a certain material as measured is 18 cm. The frequency of the
wave is 1900 Hz. Compute the speed of sound wave.
a. 342 m/s
b. 400 m/s
c. 542 m/s
d. 300 m/s
2. A horizontal cord 5 m long has a mass of 2.5 grams. What must be the tension in the cord if the
wavelength of a 120 Hz wave on it is to be 50 cm?
a. 1.50 N
b. 1.80 N
c. 2.50 N
d. 4.30 N
3. A string fixed firmly on both sides resonates at 430 Hz and 470 Hz with no resonance frequencies
in between. Find the fundamental resonance frequency.
a. 40 Hz
b. 50 Hz
c. 30 Hz
d. 60 Hz
4. A metal string under tension of 88.2 N has a length of 50 cm and mass of 0.50 gram. Determine
the frequency in the second overtone.
a. 891 Hz
b. 987 Hz
c. 790 Hz
d. 670 Hz
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5. A piano string with a length of 1.17 m and a mass of 21.0 g in under tension of 6.4 x 103 N. What
is the fundamental frequency?
a. 255 Hz
b. 187 Hz
c. 150 Hz
d. 290 Hz
6. What is the relative intensity level of sound in decibels if its intensity is 3 x 10-7 W/cm2?
a. 94.8
b. 78.7
c. 80.5
d. 75.4
7. A wave has pressure amplitude of 5 dynes/cm2 and a velocity of 35.7 m/s, what is the absolute
intensity considering that 0.001293 gm/cm?
a. 1.27 x 10-8 W/cm2
c. 3.27 x 10-8 W/cm2
b. 1.47 x 10-8 W/cm2
d. 2.71 x 10-8 W/cm2
8. A man fires a gun and hears an echo 2.4 seconds after. How far is the reflecting surface if air
temperature is 25°C?
a. 439.7 m
b. 457.4 m
c. 416.4 m
d. 354.7 m
9. A train blowing its whistle at 750 Hz approaches a station at the rate of 35 mph. What frequency is
heard by a man standing at the station considering the velocity of sound in air 1100 ft/s?
a. 739.7 Hz
b. 857.4 Hz
c. 716.4 Hz
d. 786.7 Hz
10. Two cars A and B are traveling toward each other at speeds of 45 km/.ht and 70 km/hr
respectively. If A is blowing its horn, what is the relative pitch heard by a passenger in B,
considering that the velocity of sound is 344 m/s.
a. 1.043
b. 1.021
c. 1.096
d. 1.078
11. An explosion occurs at a distance of 5 km from the observer. How long after the explosion does a
person hear if the temperature is 18°C?
a. 14.58 s
b. 12.45 s
c. 11.87 s
d. 17.54 s
12. What is the speed of sound in neon gas at temperature of 25°C considering that the molecular mass
of this gas is 20.18 kg/mol? Note: Neon is monoatomic use k = 1.67
a. 543.7 m/s
b. 478.6 m/s
c. 321.7 m/s
d. 447.5 m/s
13. What is the wavelength of yellow light whose frequency is 5 x 1014 Hz?
a. 800 nm
b. 200 nm
c. 600 nm
d. 700 nm
14. What is the angle of refraction of light as a beam of parallel light enters a block of ice at angle of
incidence 30°? Note: the angle of refraction of ice is 1.31 and air is 1.0)
a. 45°
b. 30°
c. 20°
d. 26°
15. A light ray is incident at an angle of 45° on one side of a glass plate of index of refraction 1.6. Find
its angle at which the ray emerges from the other side of the plate.
a. 26°
b. 20°
c. 22°
d. 28°
16. It was found out that the speed of light in water is 75% of its speed in vacuum. What is the index
of refraction of water?
a. 1.46
b. 1.33
c. 1.26
d. 1.67
17. A glass plate is 0.6 cm thick and has a refractive index of 1.55. Compute how long will it take for
a pulse of light to pass through the plate?
a. 4.41 x 10-12 s
b. 3.11 x 10-11 s
c. 1.34 x 10-12 s
d. 2.34 x 10-11 s
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18. A light passes from glass to water. If the index of refraction for glass is 1.54 and for water is 1.33,
compute the critical angle for this light to pass the glass
a. 59.7°
b. 45.8°
c. 67.4°
d. 50.9°
19. A layer of oil floats in water. A ray shines onto the oil with an incidence angle of 40°. At what
angle the ray makes in water if the refractive index for oil is 1.45 and for water is 1.33?
a. 34.6°
b. 28.9°
c. 21.4°
d. 30.7°
20. A light ray passing through air and strikes a glass surface at an angle of 55° from the normal
surface. What is the angle between the reflected light and the surface?
a. 55°
b. 25°
c. 35°
d. 45°
21. A light hits the surface of water in a container at an angle of 30° from the horizontal. If the index
of refraction of water is 1.33, what is the angle of refraction of the light ray?
a. 49.5°
b. 50.1°
c. 62.5°
d. 32.3°
22. Determine the focal length of the converging lens which will project the image of a lamp,
magnified 3 times, upon a screen 16 m from the lamp.
a. 3.0 cm
b. 1.4 cm
c. 2.2 cm
d. 0.7 cm
23. In what positions will a converging lens of focal length 10 cm from an image of luminous object
on a screen located 50 cm from the object?
a. 13.82 cm and 36.18 cm from the object c. 10 cm and 40 cm from the object
b. 11.52 cm and 38.48 cm from the object d. 12.56 cm and 37.44 cm from the object
24. A double convex lens has faces of radii 22 and 24 cm. When an object is 30 cm from the lens, a
real image is formed 45 cm from the lens. Compute the refractive index of the lens material.
a. 1.64
b. 1.32
c. 1.21
d. 1.76
25. Where must an object be placed in the case of a converging lens of focal length f if the image is to
be virtual and 4 times as large as the object?
a. 3/4f
b. 2/3f
c. 1/2f
d. 1/4f
26. If a beam of polarized light has one-twelfth of its initial intensity after passing through an analyzer,
what is the angle between the axis of the analyzer and the initial amplitude of the beam?
a. 65.73°
b. 76.27°
c. 73.22°
d. 67.54°
27. An observer sees a spaceship, measured 100 m long when at rest. He passed by in uniform motion
with the speed of 0.5c. While the observer is watching the spaceship, a time of 2 s elapses on a
clock on board the ship, what is the length of the moving ship?
a. 87 m
b. 85 m
c. 83 m
d. 76 m
28. The captain of a spacecraft send a pulse of light towards earth and then exactly 1 min later (as
measured by the clock on the spacecraft), sends a second pulse. An observer on earth sees the
second pulse arrive 4 minutes arrive after the first. What is the velocity of the spacecraft relative
to the earth?
a. 0.997c
b. 0.968c
c. 0.954c
d. 0.943c
29. What is the rest energy of electron equivalent to its rest mass?
a. 0.512 MeV
b. 0.987 MeV
c. 0.345 MeV
d. 0.75 MeV
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30. How much energy is needed to accelerate an electron to 0.95c?
a. 1.128 J
b. 2.345 J
c. 3.457 J
d. 0.875 J
31. What is the frequency of photon having energy of 2 eV?
a. 483 THz
b. 560 THz
c. 300 THz
d. 250 THz
32. A source is emitting 100 W green light at a wavelength of 500 nm. Compute how many photons pr
second are emitted from the source.
c. 15 x 1019 photons/s
a. 25 x 1019 photons/s
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b. 34 x 10 photons/s
d. 58 x 1019 photons/s
33. Compute the work function of sodium metal if the photoelectric threshold wavelength is 680 nm.
a. 1.83 eV
b. 3.45 eV
c. 2.14 eV
d. 1.34 eV
34. At what angle of incidence is sunlight reflected from the surface of a lake when it is fully
polarized?
a. 23°
b. 33°
c. 45°
d. 17°
35. An automobile moving at 35 m/s is approaching a building whistle with a frequency of 520 Hz. If
the speed of sound in air is 340 m/s, what is the apparent frequency of the whistle heard by the
driver?
a. 573.53 Hz
b. 543.67 Hz
c. 561.55 Hz
d. 457.54 Hz
36. Compute the speed of sound in neon gas at 27°C of molecular mass 20.18 kg/kmol and k of 1.67.
a. 454 m/s
b. 564 m/s
c. 356 m/s
d. 434 m/s
37. A magnifying glass has a lens with an index of refraction 54.4 and radii of curvature of 2.96 feet
and 4.27 feet for the two faces. What is the magnification of the lens when it is held 2.36 inches
from an object being viewed?
a. 1.6
b. 2.78
c. 2.16
d. 1.98
III. SELF-TEST
1. Find the speed of sound in 32°F if the compressibility is 3.4 x 10-6 psi.
a. 4,674 ft/sec
b. 4,764 ft/sec
c. 4,564 ft/sec
d. 4,456 ft/sec
2. The speed of compressional waves in a metal is 6,000 m/sec. What is the Young’s modulus of
elasticity for the material of the rod if the density of the material is 8.2 g/cm3?
a. 2.952 x 109 Pa b. 2.952 x 1010 Pa
c. 2.952 x 1011 Pa
d. 4.920 x 106 Pa
3. What is the wavelength of a 20-Hz sound in air at 20° and one atmosphere? (Take molecular
weight of air at STP to be 28.96)
a. 17.16 m
b. 4.48 m
c. 16.71 m
d. 8.44 m
4. A noise level meter reads the sound level in a room to be 85 dB. What is the sound intensity in the
room?
a. 1.63 x 10-4 W/m2
c. 1.63 x 10-5 W/m2
-4
2
b. 3.16 x 10 W/m
d. 3.61 x 10-5 W/m2
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5. A car moving at 20 m/sec with its horn blowing at f = 1200 Hz is chasing another car going at 15
m/sec. What is the apparent frequency of the horn as heard by the driver being chased? Take note
speed of sound to be 340 m/sec.
a. 1,219 Hz
b. 1,331 Hz
c. 1,083 Hz
d. 1,183 Hz
6. The molecular diameter of CO is 3.19 x 10-8 at 300 K and pressure of 100 mm Hg. What is the
mean free path of the gas in cm?
b. 6.86 x 10-5
c. 2.86 x 10-4
d. 6.86 x 10-6
a. 6.86 x 10-3
7. What is the average kinetic energy of a gas molecule at 0°F (-18°C)
a. 5.285 x 10-21
b. 1.057 x 10-20
c. 7.047 x 10-22
d. 3.524 x 10-19
8. What is the refractive index for a glass in which the speed of light is 124,000 miles per second?
a. 1.503
b. 1.053
c. 2.417
d. 2.741
9. An object 6 cm high is placed 12 cm away from a concave mirror whose focal length is 36 cm.
What is the height of the image?
a. 2 cm
b. 4 cm
c. 9 cm
d. 8 cm
10. How much energy is released when four 1.008145 amu particles fuse into one 4.00387 amu
particle?
a. 62.8 MeV
b. 26.8 MeV
c. 82.6 MeV
d. 750 MeV
11. Determine the energy required to give an electron a speed of 90% that of light starting from rest?
b. 1.60 x 10-11 J
c. 6.10 x 10-12 J
d. 5.25 x 10-14 J
a. 1.06 x 10-13 J
12. In order to break a chemical bond in the molecules of human skin, causing sunburn, a photon
energy of about 3.5 eV is required. To what wavelength does this corresponds?
a. 355 x 10-9 meter
c. 355 x 10-6 meter
d. 553 x 10-6 meter
b. 535 x 10-9 meter
13. What wavelength must electromagnetic radiations have if photon in the beam is to have the same
momentum as an electron moving with a speed of 2 x 105 m/sec?
a. 36.41 Ǻ
b. 3.641 Ǻ
c. 0.364 Ǻ
d. 364.1 Ǻ
14. What is the speed of compressional waves in water? The bulk modules of water is 2.2 x 10 N/m.
a. 1,483.24 m/sec
b. 130.06 m/sec
c. 741.62 m/sec
d. 341.26 m/sec
15. The difference between stagnation and static pressure in a pitot-static tube is 2.0 inch Hg. What is
the relative velocity in air at 70°F and 14.7 psia?
a. 346.7 ft/sec
b. 333.7 ft/sec
c. 444.7 ft/sec
d. 268.7 ft/sec
16. To be effective, an alarm must be heard at a minimum level 70 dB. If it is to be effective for a
man whose nearest neighbors live 200 ft down the street, what is the minimum power required?
a. 0.0023 Watt
b. 0.074 Watt
c. 4.5 Watts
d. 0.47 Watt
17. The siren of stationary fire engine has a frequency of 500 Hz, a car drives away from it at 20
m/sec. What frequency does the person in the car hears now? Take velocity of sound in still air
343 m/sec.
a. 471 Hz
b. 531 Hz
c. 445 Hz
d. 500 Hz
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Asian Power Systems Review Center
18. Find the rms speed of nitrogen molecule having M.W. = 28 kg/kmol in air at
a. 490 m/sec
b. 285 m/sec
c. 164 m/sec
d. 512 m/sec
19. Determine the volume occupied by 4 gram of oxygen at S.T.P. Molecular weight of oxygen is 32.
Standard molecular volume of any gas is 22.4 liter/mol.
a. 4.8 liters
b. 3.6 liters
c. 2.8 liters
d. 1.4 liters
20. At what pressure in Pascal will the mean free path be 50 cm for spherical molecules of radius 3 x
10-10 m? Assume ideal gas at 20C.
a. 5.06 x 10-4
b. 5.06 x 10-3
c. 6.50 x 10-3
d. 3.65 x 10-4
21. A light ray in air (nair = 1.0) is incident on a glass surface (nglass = 1.52) at an angle of 30° from the
normal. What is the angle between the refracted light ray and the normal?
a. 15.7°
b. 19.2°
c. 30°
d. 45.3°
22. An object is placed 10 cm away from a concave mirror with focal length of 30 cm. What image is
formed?
a. a real image 10 cm in front of the mirror
b. a virtual image 15 cm behind the mirror
c. a real image 20 cm in font of the mirror
d. a virtual image 25 cm behind the mirror
23. A thin lens is made from glass with n = 1.5. It has a convex face with a 25 cm radius of curvature,
and a concave face with 35 cm radius curvature. What is the focal length and type of lens?
a. diverging lens, virtual focus, f = 100 cm
b. converging lens, real focus, f = 125 cm
c. diverging lens, virtual focus, f = 150 cm
d. converging lens, real focus, f = 175 cm
24. An object is placed o.50 m from a convex mirror with a focal length of 0.2 m. What is the
magnification of the mirror?
a. 0.2857
b. 3.50
c. -0.142
d. -2.50
25. If one gram of matter could be converted entirely to energy, what would be the value of energy so
produced in kWh?
b. 2.5 x 106
c. 50 x 106
d. 5 x 106
a. 25 x 106
26. At what speed must a particle move in order to double its mass?
a. 3 x 108 m/sec
c. 2.6 x 108 m/sec
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b. 1.5 x 10 m/sec
d. 2 x 108 m/sec
27. Compute the mass of an electron traveling at half the speed of light.
a. 1.05 x 10-29 kg
c. 1.05 x 10-30 kg
-30
b. 1.25 x 10 kg
d. 1.21 x 10-30 kg
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