Sound and Music Review
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Part A: TRUE/FALSE
1. Which of the following statements are TRUE of sound waves? Identify all that apply.
- A sound wave is a mechanical wave.
- A sound wave is a means of transporting energy without transporting matter.
- Sound can travel through a vacuum.
- A sound wave is a pressure wave; they can be thought of as fluctuations in pressure with respect to time.
- A sound wave is a transverse wave.
- To hear the sound of a tuning fork, the tines of the fork must move air from the fork to one's ear.
- Most (but not all) sound waves are created by a vibrating object of some type.
- To be heard, a sound wave must cause a relatively large displacement of air (for instance, at least a cm or more) around an observer's ear.
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Answer: ABD
a. TRUE - A sound wave transports its energy by means of particle interaction. A sound wave cannot travel through a vacuum. This makes sound a mechanical wave.
b. TRUE - Absolutely! Particles do not move from the source to the ear. Particles vibrate about a position; one particle impinges on its neighboring particle, setting it in vibrational motion about its own equilibrium position.
c. FALSE - Only electromagnetic waves can travel through a vacuum; mechanical waves such as sound waves require a particle-interaction to transport their energy. There are no particles in a vacuum.
d. TRUE - As particles move back and forth longitudinally, there are times when they are very close within a given region and other times that they are far apart within that same region. The close proximity of particles produces a high pressure region known as a compression; the distancing of particles within a region produces a low pressure region known as a rarefaction. Over time, a given region undergoes oscillations in pressure from a high to a low pressure and finally back to a high pressure.
e. FALSE - Never! Waves are either longitudinal or transverse. Longitudinal waves are those in which particles of the medium move in a direction parallel to the energy transport. And that is exactly how particles of the medium move as sound passes through it.
f. FALSE - It is the disturbance that moves from the tuning fork to one's ear. the particles of the medium merely vibrate back and forth about the same location, never really moving from that location to another location. This is true of all waves - they transport energy without actually transporting matter.
g. FALSE - All sound waves are created by vibrating objects of some sort.
h. FALSE - Quite surprisingly to many, most sounds which we are accustomed to hearing are characterized by particle motion with an amplitude on the order of 1 mm or less.
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2. Which of the following statements are TRUE of sound intensity and decibel levels? Identify all that apply.
- The intensity of a sound wave has units of Watts/meter.
- When a sound wave is said to be intense, it means that the particles are vibrating back and forth at a high frequency.
- Intense sounds are characterized by particles of the medium vibrating back and forth with a relatively large amplitude.
- Intense sounds are usually perceived as loud sounds.
- The ability of an observer to hear a sound wave depends solely upon the intensity of the sound wave.
- From the least intense to the most intense, humans have a rather narrow range of intensity over which sound waves can be heard.
- The intensity of sound which corresponds to the threshold of pain is one trillion times more intense than the sound which corresponds to the threshold of hearing.
- Two sounds which have a ratio of decibel ratings equal to 2.0. This means that the second sound is twice as intense as the first sound.
- Sound A is 20 times more intense than sound B. So if Sound B is rated at 30 dB, then sound A is rated at 50 dB.
- Sound C is 1000 times more intense than sound D. So if sound D is rated at 80 dB, sound C is rated at 110 dB.
- A machine produces a sound which is rated at 60 dB. If two of the machines were used at the same time, the decibel rating would be 120 dB.
- Intensity of a sound at a given location varies directly with the distance from that location to the source of the sound.
- If the distance from the source of sound is doubled then the intensity of the sound will be quadrupled.
- If the distance from the source of sound tripled, then the intensity of the sound will be increased by a factor of 6.
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Answer: CDGJ
a. FALSE - Intensity is a power/area relationship and as such the units are typically Watts/meter2. The Watt is a unit of power and the meter2 is a unit of area.
b. FALSE - Intense sounds are simply sounds which carry energy outward from the source at a high rate. They are most commonly sound waves characterized by a high amplitude of movement. While frequency does effect one's perception of the loudness of a sound, it does not effect the intensity of a sound wave.
c. TRUE - An intense sound is the result of a large vibration of the source of sound that sets particles of the medium in motion with a high amplitude of movement about their usual rest position.
d. TRUE - Loudness is more of a subjective response to sound, dependent in part upon the quality of an observer's ears. Intensity is an objective characteristic of sound that can actually be measured in Watts/meter2. However, intense sounds will always be observed to be louder by an observer than less intense sounds.
e. FALSE - Not only must the sound be intense enough to cause an audible disturbance of the mechanisms of the ear, it also must fall within the human frequency range of 20 Hz to 20000 Hz.
f. FALSE - Humans actually have a phenomenal range of intensities to which they are sensitive to. The intensity of the sound at the threshold of pain is one-trillion times more intense than the sound at the threshold of hearing. That's quite a range.
g. TRUE - The threshold of pain has an intensity of 1 W/m2 and the threshold of hearing has an intensity of 1.0 x 10-12 W/m2. That's a ratio of one trillion.
h. FALSE - No! Since the decibel scale is based on a logarithmic function, this is simply not the case.
i. FALSE - Two sounds separated by 20 dB on the decibel scale have intensity ratios of 100:1. If one sound is 20 times more intense than another sound, then it is 13 dB higher on the decibel scale [ that comes from 10*log(20) ].
j. TRUE - Always remember that a decibel rating is based on the logarithmic function. A sound which is 1000 times (103 times) more intense than another sound is 3 bels or 30 dBels greater on the decibel scale.
k. FALSE - Two machines would produce twice the intensity; but when converted to the logarithmic scale of decibels, there decibel rating would differ by 3 dB.
l. FALSE - Intensity varies inversely with distance from the source. To be more specific, it varies inversely with the square of the distance.
m. FALSE - If the distance from the source is doubled, then the intensity is decreased by a factor of four.
n. FALSE - If the distance from the source is tripled, then the intensity is decreased by a factor of nine.
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3. Which of the following statements are TRUE of the speed of sound? Identify all that apply.
- The speed of a sound wave depends upon its frequency and its wavelength.
- In general, sound waves travel fastest in solids and slowest in gases.
- Sound waves travel fastest in solids (compared to liquids and gases) because solids are more dense.
- The fastest which sound can move is when it is moving through a vacuum.
- If all other factors are equal, a sound wave will travel fastest in the most dense materials.
- A highly elastic material has a strong tendency to return to its original shape if stressed, stretched, plucked or somehow disturbed.
- A more rigid material such as steel has a higher elasticity and therefore sound tends to move through it at high speeds.
- The speed of sound moving through air is largely dependent upon the frequency and intensity of the sound wave.
- A loud shout will move faster through air than a faint whisper.
- Sound waves would travel faster on a warm day than a cool day.
- The speed of a sound wave would be dependent solely upon the properties of the medium through which it moves.
- A shout in a canyon produces an echo off a cliff located 127 m away. If the echo is heard 0.720 seconds after the shout, then the speed of sound through the canyon is 176 m/s.
- The speed of a wave within a guitar string varies inversely with the tension in the string.
- The speed of a wave within a guitar string varies inversely with the mass per unit length of the string.
- The speed of a wave within a guitar string will be doubled if the tension of the string is doubled.
- An increase in the tension of a guitar string by a factor of four will increase the speed of a wave in the string by a factor of two.
- An increase in the linear mass density of a guitar string by a factor of four will increase the speed of a wave in the string by a factor of two.
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Answer: BFGJKNP
a. FALSE - The speed of a wave is calculated by the product of the frequency and wavelength. However, it does not depend upon the frequency and the wavelength. An alteration in the frequency or the wavelength will not alter the speed.
b. TRUE - For the same material, speed is greatest in materials in which the elastic properties are greatest. Despite the greater density of solids, the speed is greatest in solids, followed by liquids, followed by gases.
c. FALSE - Sound waves travel faster in solids because the particles of a solid have a greater elastic modulus. That is to say that a disturbance of a particle from its rest position in a solid leads to a rapid return to its rest position and as such an ability to rapidly transmit the energy to the next particle.
d. FALSE - Sound is a mechanical wave which moves due to particle interaction. There are no particles in a vacuum so sound can not move through a vacuum.
e. FALSE - Sound waves (like all waves) will travel slower in more dense materials (assuming all other factors are equal).
f. TRUE - This is the definition of elasticity. Elasticity is related to the ability of the particles of a material to return to their original position if displaced from it.
g. TRUE - A more rigid material is characterized by particles which quickly return to their original position if displaced from it. Sound moves fastest in such materials.
h. FALSE - The speed of sound through a material is dependent upon the properties of the material, not the characteristics of the wave.
i. FALSE - A loud shout will move at the same speed as a whisper since the speed of sound is independent of the characteristics of the sound wave and dependent upon the properties of the material through it is moving.
j. TRUE - The speed of sound through air is dependent upon the temperature of the air.
k. TRUE - This is a big principle. Know it.
l. FALSE - Speed is distance traveled per time. For this case, the sound travels a distance of 254 m (to the cliff and back) in 0.720 seconds. That computes to 353 m/s.
m. FALSE - For a guitar string, the equation for the speed of waves is v = SQRT (Ftens/mu). From the equation, it is evident that an increase in tension will result in an increase in the speed; they are directly related.
n. TRUE - For a guitar string, the equation for the speed of waves is v = SQRT (Ftens/mu). From the equation, it is evident that an increase in mass per unit length (mu) will result in an decrease in the speed; they are inversely related.
o. FALSE - The speed of a wave in a guitar string varies directly with the square root of the tension. If the tension is doubled, then the speed of sound will increase by a factor of the square root of two.
p. TRUE - The speed of a wave in a string is directly related to the square root of the tension in the string. So the speed will be changed by the square root of whatever factor the tension is changed.
q. FALSE - An increase in the linear mass density by a factor of four will decrease the speed by a factor of 2. The speed is inversely related to the square root of the linear density.
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4. Which of the following statements are TRUE of the frequency of sound and the perception of pitch? Identify all that apply.
- A high pitched sound has a low wavelength.
- A low-pitched sound is a sound whose pressure fluctuations occur with a low period.
- If an object vibrates at a relatively high frequency, then the pitch of the sound will be low.
- The frequency of a sound will not necessarily be the same as the frequency of the vibrating object since sound speed will be altered as the sound is transmitted from the object to the air and ultimately to your ear.
- Two different guitar strings are used to produce a sound. The strings are identical in terms of material, thickness and the tension to which they are pulled. Yet string A is shorter than string B. Therefore, string A will produce a lower pitch.
- Both low- and high-pitched sounds will travel through air at the same speed.
- Doubling the frequency of a sound wave will halve the wavelength but not alter the speed of the wave.
- Tripling the frequency of a sound wave will decrease the wavelength by a factor of 6 and alter the speed of the wave.
- Humans can pretty much hear a low-frequency sound as easily as a high-frequency sound.
- Ultrasound waves are those sound waves with frequencies less than 20 Hz.
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Answer: AFG
a. TRUE - High pitch corresponds to a sound with high frequency and therefore low wavelength.
b. FALSE - Low pitched sound have a low frequency. Frequency is inversely related to period. So low pitched sounds have a high period. That is, the time for the vibrations to undergo one complete cycle is large for a low frequency (or low pitch) sound.
c. FALSE - Pitch is a subjective response of the ear to sound. Frequency is an objective measure of how often the sound undergoes an oscillation from high to low pressure. The two are related in the sense that a sound with a high frequency will be perceived as a sound with a high pitch.
d. FALSE - As waves (of any type) are transmitted from one medium to another, the speed and the wavelength can be altered, but the frequency will not be changed. Thus, the frequency of the source is the frequency of the sound waves which impinge upon the ear.
e. FALSE - The strings are identical in terms of their properties; this means that waves travel at the same speed through each. Yet string A is shorter than string B, so the wavelengths of waves are shortest in string A. As such, the frequencies are greatest for string A and it is observed to produce sounds of higher pitch.
f. TRUE - The speed at which waves travel through air is dependent upon the properties of the air and not the properties of the wave.
g. TRUE - Frequency and wavelength are inversely related; doubling one will halve the other. Yet the speed of a wave is independent of each.
h. FALSE - Tripling the frequency of a sound wave will make wavelength decrease by a factor of 3 but not alter the speed of a wave.
i. FALSE - The response of the ear to sound is dependent in part on the frequency of the sound. A higher pitch sound of the same intensity is generally heard to be louder than a lower pitch sound of the same intensity.
j. FALSE - Ultrasound waves are waves which have a frequency beyond the human range of audible frequencies - above 20000 Hz.
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5. Which of the following statements are TRUE of standing wave patterns? Identify all that apply.
- A standing wave pattern is formed as a result of the interference of two or more waves.
- When a standing wave pattern is established, there are portions of the medium which are not disturbed.
- A standing wave is really not a wave at all; it is a pattern resulting from the interference of two or more waves which are traveling through the same medium.
- A standing wave pattern is a regular and repeating vibrational pattern established within a medium; it is always characterized by the presence of nodes and antinodes.
- An antinode on a standing wave pattern is a point which is stationary; it does not undergo any displacement from its rest position.
- For every node on a standing wave pattern, there is a corresponding antinode; there are always the same number of each.
- When a standing wave pattern is established in a medium, there are alternating nodes and antinodes, equally spaced apart across the medium.
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Answer: ABCDG
a. TRUE - Interference results when two (or more) waves interfere to produce a regular and repeating pattern of nodes and antinodes. The presence of the nodes standing still along the medium at the same position is what gives it its name of "standing" wave.
b. TRUE - Standing wave patterns are characterized by the presence of nodes - points of no disturbance.
c. TRUE - This is correct. When a standing wave pattern is being observed, it is an interference pattern - a pattern of the medium resulting from two or more waves interfering to produce the very visible pattern.
d. TRUE - This is probably a good definition of a standing wave pattern.
e. FALSE - Nodes are points which are stationary and undergoing no displacement. The antinodal positions of a standing wave pattern undergo oscillation from a maximum positive displacement to a maximum negative displacement.
f. FALSE -This would be a true statement for standing wave patterns formed in closed-end resonance air columns. Yet for guitar strings and open end air columns, there is always one more node than antinode.
g. TRUE - This is a good way to describe what is seen in the pattern.
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6. Which of the following statements are TRUE of the concept of resonance? Identify all that apply.
- A musical instrument can play any frequency imaginable.
- All musical instruments have a natural frequency or set of natural frequencies at which they will vibrate; each frequency corresponds to a unique standing wave pattern.
- The result of two objects vibrating in resonance with each other is a vibration of larger amplitude.
- Objects which share the same natural frequency will often set each other into vibrational motion when one is plucked, strummed, hit or otherwise disturbed. This phenomenon is known as a forced resonance vibration.
- A vibrating tuning fork can set a second tuning fork into resonant motion.
- The resonant frequencies of a musical instrument are related by whole number ratios.
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Answer: BCDE(mostly)F
a. FALSE - An instrument which is truly musical can only play a specific set of frequencies, each one corresponding to a standing wave pattern with which that instrument can vibrate. (Of course, one could make a case that by modifying properties of the instrument, small adjustments could be made in the speed at which the waves might move and thus allow the instrument to produce about any frequency imaginable.)
b. TRUE - The frequencies at which an instrument would naturally vibrate are known as its harmonics. Each frequency corresponds to a unique standing wave pattern.
c. TRUE - Resonance results in a big vibration because two waves are now interfering in a regular manner to produce a resultant wave with a large amplitude of vibration.
d. TRUE - This is a good definition of resonance vibrations.
e. TRUE - This can happen provided that the two tuning forks have the same natural frequency and that they are somehow connected (for instance by air).
f. TRUE - The frequencies at which an instrument would naturally vibrate are known as its harmonics. The frequency of each harmonic is a whole number multiple of the fundamental frequency. As such, every frequency in the set of natural frequency is related by whole number rations.
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7. Which of the following statements are TRUE of the harmonics and standing wave patterns in guitar strings? Identify all that apply.
- The fundamental frequency of a guitar string is the highest frequency at which the string vibrates.
- The fundamental frequency of a guitar string corresponds to the standing wave pattern in which there is a complete wavelength within the length of the string.
- The wavelength for the fundamental frequency of a guitar string is 2.0 m.
- The wavelength for the second harmonic played by a guitar string is two times the wavelength of the first harmonic.
- The standing wave pattern for the fundamental played by a guitar string is characterized by the pattern with the longest possible wavelength.
- If the fundamental frequency of a guitar string is 200 Hz, then the frequency of the second harmonic is 400 Hz.
- If the frequency of the fifth harmonic of a guitar string is 1200 Hz, then the fundamental frequency of the same string is 6000 Hz.
- As the frequency of a standing wave pattern is tripled, its wavelength is tripled.
- If the speed of sound in a guitar string is 300 m/s and the length of the string is 0.60 m, then the fundamental frequency will be 180 Hz.
- As the tension of a guitar string is increased, the fundamental frequency produced by that string is decreased.
- As the tension of a guitar string is increased by a factor of 2, the fundamental frequency produced by that string is decreased by a factor of 2.
- As the linear density of a guitar string is increased, the fundamental frequency produced by the string is decreased.
- As the linear density of a guitar string is increased by a factor 4, the fundamental frequency produced by the string is decreased by a factor of 2.
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Answer: EFLM
a. FALSE - The fundamental frequency is the lowest possible frequency which an instrument will play.
b. FALSE - For a guitar string, the standing wave pattern for the fundamental frequency is one in which there is one-half wavelength within the length of the string.
c. FALSE - The wavelength for the fundamental frequency is two times the length of the string (not 2.0 m).
d. FALSE - The wavelength of the second harmonic is one-half the length of the wavelength of the fundamental (the frequency of the second harmonic is twice the frequency of the fundamental).
e. TRUE - The fundamental frequency is the lowest possible frequency and the longest possible wavelength with which an instrument will vibrate.
f. TRUE -The frequency of the nth harmonic is n times larger than the frequency of the fundamental or first harmonic.
g. FALSE - The frequency of the fundamental would be 240 Hz if the frequency of the fifth harmonic is 1200 Hz.
h. FALSE - If the frequency is tripled, then the wavelength is one-third as much.
i. FALSE - The fundamental frequency would be 250 Hz. The wavelength of the fundamental is two times the length of the string - 1.2 m. And the frequency of the fundamental is the speed divided by the wavelength of the fundamental.
j. FALSE - As the tension of a guitar string is increased, the speed of vibrations in the string is increased and the frequency will be increased.
k. FALSE - If the tension in a guitar string is increased by a factor of 2, then the speed of vibrations in the string will be increased by a factor of the square root of 2 (1.41) and the frequency will be increased by a factor of 1.41.
l. TRUE - If the linear density of a guitar string is increased, then the speed of vibrations in the string will be decreased and the frequency will be decreased.
m. TRUE - If the linear density of a guitar string is increased by a factor of 4, then the speed of vibrations in the string will be decreased by a factor of the square root of 4 (2.0) and the frequency will be decreased by a factor of 2.
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8. Which of the following statements are TRUE of the harmonics and standing wave patterns in air columns? Identify all that apply.
- The speed of the waves for the various harmonics of open-end air columns are whole number multiples of the speed of the wave for the fundamental frequency.
- Longer air columns will produce lower frequencies.
- The pitch of a sound can be increased by shortening the length of the air resonating inside of an air column.
- An open end of an air column allows air to vibrate a maximum amount whereas a closed end forces air particles to behave as nodes.
- Open-end air columns have antinodes positioned at each end while closed-end air columns have nodes positioned at each end.
- Closed-end air columns can only produce odd-numbered harmonics.
- Open-end air columns can only produce even-numbered harmonics.
- A closed-end air column that can play a fundamental frequency of 250 Hz cannot play 500 Hz.
- An open-end air column that can play a fundamental frequency of 250 Hz cannot play 750 Hz.
- A closed-end air column has a length of 20 cm. The wavelength of the first harmonic is 5 cm.
- An open-end air column has a length of 20 cm. The wavelength of the first harmonic is 10 cm.
- Air column A is a closed-end air column. Air column B is an open-end air column. Air column A would be capable of playing lower pitches than air column B.
- The speed of sound in air is 340 m/s. An open-end air column has a length of 40 cm. The fundamental frequency of this air column is approximately 213 Hz.
- The speed of sound in air is 340 m/s. A closed-end air column has a length of 40 cm. The fundamental frequency of this air column is approximately 213 Hz.
- If an open-end air column has a fundamental frequency of 250 Hz, then the frequency of the fourth harmonic is 1000 Hz.
- If a closed-end air column has a fundamental frequency of 200 Hz, then the frequency of the fourth harmonic is 800 Hz.
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Answer: BCDFHLNO
a. FALSE - It is the frequency (not the speed) of the various harmonics which are whole number multiples of the fundamental frequency.
b. TRUE - Assuming that two air columns are of the same type (both open- or both closed), the standing wave patterns of the longer air column would have longer wavelengths and thus lower frequencies and pitch.
c. TRUE - As the length of an air column is shortened, the wavelengths are decreased and the frequencies are increased.
d. TRUE - This is exactly the case and is clearly portrayed in the standing wave patterns which are constructed for air columns.
e. FALSE - A closed-end air column is an air column with one end open and one end closed. It is the closed end which is characterized by a nodal position but the open end is characterized by an antinode.
f. TRUE - Closed-end air columns produce a first, third, fifth, seventh, etc. harmonic - all odd numbers.
g. FALSE - Open-end air columns can produce all harmonics - first, second, third, fourth, etc.
h. TRUE - If a closed-end air column has a fundamental frequency of 250 Hz, then the other frequencies in the set of natural frequencies are 750 Hz, 1250 Hz, 1750 Hz, etc. It can only have odd-numbered harmonics.
i. FALSE - If an open-end air column has a fundamental frequency of 250 Hz, then the other frequencies in the set of natural frequencies are 500 Hz, 750 Hz, 1000 Hz, 1250 Hz, etc. An open-end air column can produce all the harmonics.
j. FALSE - The wavelength of the first harmonic of a closed-end air column is four times the length of the air column - 80 cm.
k. FALSE - The wavelength of the first harmonic of an open-end air column is two times the length of the air column - 40 cm.
l. TRUE (sort of) - For the same length (the sort of part), a closed-end air column would have standing waves which are longer and therefore have frequencies which are lower.
m. FALSE - If the length of this open-end air column is 40 cm, then the wavelength of the fundamental is 0.80 m. The frequency of the fundamental is (340 m/s)/(0.8 m) = 425 Hz.
n. TRUE - If the length of this closed-end air column is 40 cm, then the wavelength of the fundamental is 1.60 m. The frequency of the fundamental is (340 m/s)/(1.6 m) = 213 Hz.
o. TRUE - The frequency of the fourth harmonic is four times the frequency of the first harmonic.
p. FALSE - A closed-end air column cannot have a fourth harmonic; there are only odd-numbered frequencies.
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9. Which of the following statements are TRUE of sound interference and beats? Identify all that apply.
- Beats result when two sounds of slightly different frequencies interfere.
- Beats are characterized by a sound whose frequency is rapidly fluctuating between a high and a low pitch.
- Two sounds with a frequency ratio of 2:1 would produce beats with a beat frequency of 2 Hz.
- Two tuning forks are sounding out at slightly different frequencies - 252 Hz and 257 Hz. A beat frequency of 5 Hz will be heard.
- A piano tuner is using a 262 Hz tuning fork in an effort to tune a piano string. She plucks the string and the tuning fork and observes a beat frequency of 2 Hz. Therefore, she must lower the frequency of the piano string by 2 Hz.
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Answer: AD
a. TRUE - This is the number one criteria for the formation of audible beats.
b. FALSE - Beats are characterized by sounds which are rapidly oscillating between high and low levels of loudness due to fluctuations in the amplitude of the resulting wave.
c. FALSE - Two sounds with a frequency difference (not ratio) of 2 Hz will produce a bear frequency of 2 Hz.
d. TRUE - The beat frequency is the frequency at which the amplitude of the oscillations increase and decrease. This beat frequency is always the difference in frequency of the two sounds which interfere to create the beats.
e. FALSE - She must either lower or increase the frequency of the piano string by 2 Hz.
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Navigate to:
Review Session Home - Topic Listing
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Answers to Questions: All || #1-#9 || #10-#52 || #53-#64 || #65-#75
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