Understanding Vocabulary
Section 20.1
1. transverse waves
2. trough
3. fundamental
4. waves
5. longitudinal waves
6. harmonics
Section 20.2
7. circular wave
8. reflection
9. diffraction
10. absorption
Section 20.3
11. constructive interference
12. destructive interference
Reviewing Concepts
Section 20.1
1. Answers are:
a. wave motion; vibration of air transformed to electromagnetic
wave and transmitted.
b. wave motion; energy released in the earthquake is transmitted
over ground to the floor of the house.
c. wave motion; electromagnetic signal is transformed by the
speaker to sound wave.
d. wave motion; X rays are a form of electromagnetic waves
e. wave motion; visible light is a form of electromagnetic waves
2. Transverse waves vibrate perpendicular to the direction in which the
wave travels. Examples include light, X rays, water waves.
Longitudinal waves vibrate parallel to the direction in which the wave
travels. Examples include sound and the P-wave of an earthquake.
3. Answers are:
a. v = fλ
b. λ = v ÷ f
c. f = v ÷ λ
4. speed = wavelength ÷ period
5. very short wavelength - electromagnetic waves
very long wavelength - water waves
6. D shows amplitude; C shows wavelength
7. A standing wave occurs when an object vibrates at multiples of the
resonant frequency. Standing waves occur as a result of reflected
energy at a boundary between two media.
8. three nodes and two antinodes
10. Answers are:
A reflection
B absorption
C diffraction
D refraction
11. The amplitude of the wave decreases as it is absorbed.
12. The interaction between the wave and an opening which is small
compared to the wavelength causes the wave to pass through a small
opening and spread out as a circular wave front behind the opening.
13. Answers are:
a. refraction
b. diffraction
c. reflection
d. absorption
e. absorption
Section 20.3
14. The superposition principle states that the total vibration at any point
is the sum of the vibrations of the individual waves. So, the resulting
amplitude will be the sums of the amplitudes of the two individual
waves.
15. Yes, if the amplitudes of the two waves are identical and they
interfere destructively, the resulting wave will have no amplitude.
16. Answers are:
a. The amplitude of the resulting wave is the sum of the amplitudes
of the interfering waves.
b. The amplitude of the resulting wave is the difference between
the amplitudes of the interfering waves.
Solving Problems
Section 20.1
1. v = fλ = (10 Hz)(2 m) = 20 m/sec
2. λ = v ÷ f = (400 m/sec) ÷ (200 Hz) = 2 m
3. f = v ÷λ = (5 m/sec) ÷ (1 m) = 5 Hz
T = 1/f = 1/5 Hz = 0.2 Hz
4. velocity = frequency × wavelength = 10 Hz × 0.08 m = 0.8 m/sec
5. Answers are:
a. period = 1/frequency = 1/(30 Hz) = 0.033 sec
b. 60 Hz
c. 75 Hz
d. 3 nodes
e. 2 antinodes
6. Third harmonic = sixth harmonic divided by 2 = 48 Hz ÷ 2 = 24 Hz
7. The fourth harmonic has 5 nodes and 4 antinodes.
8. The second harmonic = 2 times fundamental = 2 × 440 Hz = 880 Hz
Section 20.2
9. The answer is:
Section 20.3
10. A
11. C
Applying Your Knowledge
Section 20.1
1. Answers are:
a. transverse
b. 0.000278 Hz
c. speed = wavelength ÷ period
wavelength = period × speed = (3,600 sec)(200 m/sec)
wavelength = 720,000 meters = 720 kilometers
2. When a baseball hits a bat, standing
waves occur along the bat. If a ball hits at
the sweet spot, both the fundamental and
2nd harmonic waves occur. The sweet
spot is between the locations of the nodes
of these vibrations, about 17 centimeters
from the barrel end of the bat. If the ball
hits at another position, the bat vibrates
with a relatively large amplitude that
hurts your hands. If the ball hits the sweet
spot, the vibrations have lower
amplitudes and there is no stinging
sensation after you hit the ball.
Section 20.2
3. Answers are:
a. The electromagnetic wave of visible light coming from the eye
chart is being refracted.
b. Light waves
c. Eyes that are near- or farsighted do not refract light in a way that
brings image into focus on the retina. Eyeglasses correct this
problem by refracting light so that when it enters the eye images
are in focus on the retina.
4. The sound must travel from the source to the wall, 34 meters, and
back again, a total of 68 meters.
time delay = (distance ÷ speed) = (68 m) ÷ (340 m/sec) = 0.2 sec
Section 20.3
5. If two waves are superimposed in such a way that their crests are in
phase, the amplitude of their resultant wave crest will be the sum of
the amplitude of the two waves. A wave twice the height of the
normal ocean waves could form if the conditions were right.
6. Answers may vary. Brief sample answers:
a. Airport noise: Noise pollution from airports is considered to be
an environmental problem. There are certain special interest
groups who work specifically to reduce noise pollution from
airports. Ways that airport noise can be reduced include
modifying airplane engines to reduce sound produced and
making sure that the area around an airport includes open space
so that the loud noise has farther to travel before affecting
people. Also, airports are designed so that the people inside do
not hear the noise being made by the plane on the runway. The
main solution for reducing sound in this situation is by absorbing
the sound.
b. Highway noise: Sound barriers are often constructed at the edges
of highways to absorb the traffic noise. Usually they occur when
the highway occurs in residential areas. Also, whenever new
highway projects are proposed, noise studies are performed to
see how the project will affect noise levels in local areas. The
following link to this government site provides interesting
information about highway traffic noise: http://
www.fhwa.dot.gov/environment/htnoise.htm. The main solution
for reducing sound in this situation is by absorbing sound.
c. Teenage hearing protection: Here a student could design a
survey to give to students in the school. The objective of the
survey would be to learn (1) whether or not teenagers protect
their hearing when exposed to loud noises (such as at rock
concerts, or in rural areas when farm machinery is in use), and
(2) how regularly they use hearing protection.
d. Noise/health: The primary cause of hearing loss is due to noise.
Hearing damage is permanent. Noise pollution during the night
can cause sleep loss when can adversely affect health. Chronic
loud noise is thought to increase stress levels in people. Long
term stress due to loud noise or any other source can ultimately
have deleterious health effects.
Understanding Vocabulary
Section 21.1
1. decibels
2. acoustics
3. pitch
4. supersonic
5. Doppler effect
6. shock wave
Section 21.2
7. reverberation
8. Fourier’s theorem
Section 21.3
9. cochlea
10. scales
11. beat
12. consonance
13. dissonance
14. sonogram
Reviewing Concepts
Section 21.1
1. You would not hear the explosion because in the vacuum of space
does not have a continuous medium for carrying the longitudinal
wave. Sound needs air molecules and bits of matter to carry the sound
waves.
2. The sound of people’s voices is a complex sound, created by the
superposition of many frequencies and harmonics. The nerves in the
ear respond separately to each different frequency with the brain
interpreting the signals. Meaning in different sounds or voices is
derived from the patterns of frequency and loudness and softness.
3. The decibel scale measures the loudness (or amplitude) of sound and
is measured on a scale of 1 to 100. Note: the scale is logarithmic,
which advanced students may recognize.
4. Moving toward you, the pitch will increase.
5. The airplane needs to travel faster than the speed of sound. This speed
is referred to as supersonic.
6. Stereo sound is two recordings, one played from the right speaker and
one from the left speaker. The “live” sound is created by the slight
differences in phase between sound reaching your left and right ears.
This is how you would experience the sound if it were played live.
Section 21.2
7. Sound is caused by the vibration of the molecules of a substance,
most commonly air, at frequencies within the range of hearing. As
sound travels through a mass of molecules, it causes molecules to
oscillate between being tightly packed and more spread out.
However, the molecules do not travel with the sound but vibrate in
place.
8. Longitudinal
9. If the pressure of a gas is increased in one area, the gas particles tend
to spread out and lower the pressure in surrounding areas. The gas
atoms have mass, and therefore inertia. The combination of inertia
and restoring force from pressure causes gas molecules to exhibit
harmonic motion in the form of sound waves.
10. d; frequency and wavelength are inversely proportional. The sound
with the highest frequency will have the shortest wavelength.
11. When temperature of a material increases, the speed of sound through
that material increases. This is because the molecules in the material
move faster at higher temperatures and sound depends on the
movement of molecules. Also, the speed of sound is calculated by
multiplying frequency and wavelength. Therefore, because the
frequency of the sound stays the same, at higher temperatures,
wavelength must increase.
12. In your classroom, because the acoustics indoors allow sound to be
reflected, creating reverberation which adds to the direct sound.
Outdoors, sound has few barriers and the sound waves continue to
spread out.
Section 21.3
13. A wave form graph relates how pressure changes over time for a
complex sound. This graph shows the harmonic motion of sound. A
spectrum graph is a picture of all the different frequencies that make
up a complex sound. From this graph, you can identify the loudest
frequencies (based on amplitude) and the quietest frequencies.
14. Musicians wear earplugs to avoid damage to their ears from the
constant loud noise of the band or orchestra with which they are
performing. Listening to loud sounds for an extended period of time
may cause the tiny, sound conducting hairs of the middle ear to
weaken or break off, causing a loss of hearing.
15. The eardrum
16. Pitch is how high or low we hear frequency. They are directly
proportional, but pitch depends upon the human ear and brain.
17. The sound from an instrument is not a pure frequency, but consists of
a characteristic pattern of harmonics. As the instrument reproduces a
certain fundamental frequency, it is accompanied by the unique
pattern of harmonics characteristic of the instrument.
18. When two sound frequencies are close, but not the same, the phase of
the combination of waves creates an oscillation of the loudness of the
sound, or beat. The more closely matched the frequencies are, the
higher the beat count.
19. The limits of human hearing are approximately 20,000 Hz, while a
dog’s hearing is sensitive to a higher range of frequencies, including
25,000 Hz.
Solving Problems
Section 21.1
1. Answers are:
a. The ordinary conversation sounds twice as loud as the sound in a
restaurant.
b. The amplitude of the waves is 10 times greater.
2. The star would be moving away from you if the star gave off red
light, because the frequency would be lower.
Section 21.2
3. wavelength = speed ÷ frequency
wavelength = (340 m/sec) ÷ (680 Hz) = 0.5 meters
4. The longest wavelength occurs at the lowest frequency, 20 Hz.
wavelength = speed ÷ frequency
wavelength = (340 m/sec) ÷ (20 Hz) = 17 meters. Using the same
formula and 20,000 hertz, the shortest wavelength is 0.017 meters.
5. The time it takes to travel over and back is the time it takes to travel
340 meters.
time = 2 × (distance ÷ speed) = 2 × (170 m ÷ 340 m/sec) = 1 sec
6. wavelength of the fundamental = 4 × length of pipe
wavelength of fundamental = 4 × (1 meter) = 4 m
frequency = wave speed ÷ wavelength = (340 m/sec) ÷ (4 m)
frequency = 85 Hz
Section 21.3
7. Octaves are multiples of the original frequency.
The frequency of the C one octave higher: 528 Hz
The frequency of the C one octave lower: 132 Hz
8. You would hear oscillations of loudness called beats. These beats are
unpleasant sounding.You would hear beats at a frequency of 3 beats
per second.
Applying Your Knowledge
Section 21.1
1. Perfect pitch is the ability to identify or produce a note without a
reference note. Often musicians will use a tuning fork to help them
tune their instrument. A person with perfect pitch would be able to
tune without using the tuning forks. The pros of having perfect pitch
are that people with it tend to have an easier time learning music and
may have likely started learning music at a young age.The cons of
perfect pitch are that a person with it hears when notes are wrong.
This sensitivity can be very frustrating when other people around the
person aren’t as sensitive. This is true more often than not because
perfect pitch is a rare condition. Also, a person with perfect pitch
hears all sounds (car horns, machine sounds, etc.) as notes and can’t
“tune off” this awareness. Again, this sensitivity can lead to a lot of
tension and frustration.
Section 21.2
2. Curtains absorb sound waves. Absorption decreases the amplitude of
a wave. For sound waves, amplitude is related to loudness, so
absorption decreases the loudness of sound waves. The loudness of
sound in a room can be reduced by hanging heavy curtains.
3. The superposition principle states that complex sound is created by
the superposition of many frequencies: wave A + wave B = complex
wave D. For example, the human voice is the result of
superposition—a voice contains thousands of different frequencies.
Fourier’s theorem states that any wave form can be represented as a
sum of single frequency waves: complex wave C = wave A + wave B.
Section 21.3
4. Active noise reduction (ANR) is used widely in noisy places such as
airplane cockpits where the noise is mechanical due to the airplane
engine. ANR headphones contain a microphone that picks up outside
noise and electronically inverts the sound waves of the noise. A
speaker in the headphones then plays the inverted waves, allowing
destructive interference to “cancel out” the outside sounds to your
ears. Ear plugs and ear muffs work by absorbing the sound and
effectively reduce its amplitude or loudness. This type of hearing
protection is “passive” and more useful when the noise is coming
from many different sources.
5. Exposure to sounds greater than 85-100 dB for extended periods of
time can damage the ear. Short burst of sound greater than 140 dB can
also damage the ear. The damage to the ear is cumulative and
permanent, so it is important to protect your ears from loud noises.
You can protect your hearing by avoiding loud noises and high
frequency sounds. Different types of hearing protection include:
earmuffs, which fit over the outer ear, earplugs which fit directly into
the ear canal, and the Active Noise Reduction (ANR) protection.
Places that have excessive noise require hearing protection. Examples
include outdoors at airports, environments where power tools or
heavy machinery are used, and loud concerts.
6. The word “synthesize” means “to put together”, and that is how these
electronic instruments work. The sound of each instrument is
synthesized by programming a recipe of harmonics and specifying
the rise and fall time for each frequency. A good synthesizer may use
64 different frequencies for each note to simulate an instrument
sound.
7. Male voices start around 100 Hz and female voices around 200 Hz,
extending up to about 3,000 Hz for a baby’s shrill cry. The human
voice range is close to the most sensitive range (200-2,000 Hz) within
the range of human hearing.