Chapter 7: Waves and Sound

Question 1

What is a sinusoidal wave? Which ways can sinus sinusoidal propagate?

Answer 1

A sinusoidal wave or a wave in which part particles oscillate back-and-forth with a displacement that follows a sinusoidal pattern. There are transverse and longitudinal sinusoidal waves.

Question 2

What is a transverse wave? Is sound a transverse wave? Give examples of a transverse wave.

Answer 2

A transverse wave are those in which the direction of particle oscillation is perpendicular to the propagation of the wave.

Sound is not a transverse wave, sound is a longitudinal wave.

Examples of transverse waves are electromagnetic waves such as microwaves, x-rays, and visible light.

Question 3

What is a longitudinal wave? Is sound a longitudinal wave?

Answer 3

Longitudinal waves are ones in which the particles of the wave of oscillate parallel to the direction of propagation, that is the wave of particles are oscillating in the direction of energy transfer.

Sound waves are classic example of longitudinal waves.

Question 4

Regarding energy transfer, describe transverse and longitudinal waves.

Answer 4

Transverse waves have particle oscillation perpendicular to the direction of propagation and energy transfer.

Longitudinal waves have particle, oscillation, parallel to the direction of propagation and energy transfer.

In any way form, energy is delivered in the direction of wave travel.

Question 5

What is wavelength, what is frequency, what is hertz?

Answer 5

Wavelength is the distance from one maximum (crest) of the wave to the next.

Frequency is the number of wavelengths passing a fixed point per second.

Hertz is a measurement of cycles per second.

Question 6

How do we calculate the propagation speed of a wave?

Answer 6

Question 7

Frequency defines the number of cycles per second. What is its inverse?

Answer 7

If frequency defines the number of cycles per second, then it’s inverse (PERIOD T) is the number seconds per cycle:

Question 8

What is angular frequency (w)?

Answer 8

Angular frequency is measured in radians per second and is often used in consideration of simple harmonic motion in springs and pendula:

Question 9

What is equilibrium position, displacement (x), amplitude, crest, trough, wavelength?

Answer 9

Waves oscillate about a central point called the equilibrium position.

The displacement in a wave describes how far a particular point on the wave is from the equilibrium position, expressed as a vector quantity.

The maximum magnitude of displacement in a wave is called its amplitude (A).

Question 10

What is the phase difference of a wave? What does it mean when we say that waves are in phase or out of phase?

Answer 10

We can describe how in step or out of steps waves are by calculating the phase difference. If we consider two waves that have the same frequency, wavelength, and amplitude, and that pass through the same space at the same time, we can say that they are in phase if they’re respective crests and troughs coincide (line up with each other other). When waves are perfectly in phase, we say that the phase difference is zero.

However, if the two waves travel through the same space in such a way that the crest of one wave of coincide with the troughs of the other, then we would say that they are out of phase, and the phase difference would be one half of a wave. (Lamda/2 or 180°). One cycle equals one wavelength equals 360°.

Question 11

What is the principle of superposition? What is constructive interference? What is destructive interference?

Answer 11

The principle of superposition states that when waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacement of the two interacting waves.

When the waves are in phase, the displacement always add together, and the amplitude of the resultant is equal to the sum of the amplitude of the two waves. This is called constructive interference.

When waves are out of phase, the displacement always counteract each other, and the amplitude of the result and wave is the difference between the amplitude of the interacting waves. This is called destructive interference.

Question 12

What are the common audible frequencies to young adults?

Answer 12

The frequencies between 20 Hz and 20,000 Hz or commonly audible to young adult adults, and high frequency hearing generally declines with age.

Question 13

What is damping or attenuation?

Answer 13

Damping or attenuation is a decrease in amplitude of a wave caused by an applied or non-conservative force.

Question 14

MCAT concept check General wave characteristics 7.1 page 256 question one

Answer 14

Wave speed is the rate which a wave transmits the energy or matter it is carrying. Wave speed is the product of frequency and wavelength.

Frequency is a measure of how often a waveform passes a given point in space. It is measured in Hertz.

Angular frequency is the same as frequency, but is measured in radians per second.

Period is the time necessary to complete a wave cycle.

The equilibrium position is the point with zero displacement in an oscillating system.

Amplitude is the maximum displacement of a wave from the equilibrium position.

Traveling waves have nodes in anti nodes that move with wave propagation.

Standing waves have defined nodes and anti-nodes that do not move with wave propagation.

Question 15

What is a node? What is an anti-node?

Answer 15

Points in the wave that remain at rest where amplitude is constantly zero are known as nodes.

Points midway between the nodes fluctuate with maximum amplitude and are known as anti-nodes.

Question 16

MCAT concept check General wave characteristics 7.1 page 256 question 2

Answer 16

If two waves are perfectly in phase, the amplitude of the resulting wave is equal to the sum of the amplitude of the interfering waves.

If two waves are perfectly out of phase, the amplitude of the resulting wave is the difference of the amplitude of the interfering waves.

Therefore, if the two waves are anywhere between these two extremes, the amplitude of the resulting wave will be somewhere between the sum and difference of the amplitude of the interfering waves

Question 17

MCAT concept check General wave characteristics 7.1 page 256 question 3

True or false: sound waves are a prime example of transverse waves.

Answer 17

False. Sound waves are a prime example of longitudinal waves.

Question 18

MCAT concept check General wave characteristics 7.1 page 256 question 4

How does applying a force at the natural frequency of a system change the system?

Answer 18

The object will resonate because the force frequency each equals the natural (resonant) frequency. The amplitude of the oscillation will increase.

Question 19

What is the resonant frequency of an object?

Answer 19

The resonant frequency of an object is the natural frequency of the object. Any solid object when struck hit rubbed or disturbed in anyway will begin to vibrate. If the natural frequencies within the frequency detection range of the human ear, the sound will be audible.

Question 20

What is the scientific academic description of sound?

Answer 20

Sound is a longitudinal wave transmitted by the oscillation of particles in a deformable medium. As such, sound can travel through solid liquids and gases, but cannot travel through a vacuum.

Question 21

What is the equation for the speed of sound?

Answer 21

Question 22

The speed of sound can be given by the following equation:

What is the bulk modulus (B)? What has the lowest and highest bulk modulus?

Answer 22

The bulk modulus is a measure of the medium’s resistance to compression.

B increases from gas to liquid to solid.

Solid has the highest bulk modulus, gas has the lowest bulk modulus.

Question 23

Given the equation for the speed of sound shown in the image, in which medium does sound travel the fastest, and the slowest (solid, liquid, gas; high or low density)

Answer 23

The speed of sound is fastest in a solid with low density, and slowest in a gas with high density.

Question 24

What is the speed of sound in air at 20°C?

Answer 24

Approximately 343 m/s.

Question 25

What is rarefaction?

Answer 25

Rarefaction is decompression. Sound is produced by the mechanical disturbance of particles and material along the sound waves direction of propagation. Although the particles themselves do not travel along with the wave, they do vibrate or oscillate about an equilibrium position, which causes small regions of compression to alternate with small regions of rarefaction

Question 26

What is pitch? Again what is the normal range of human hearing?

Answer 26

Our perception of the frequency of sound is called the pitch. Lower frequency sounds of lower pitch, higher frequency sounds of higher pitch. A normal range of human hearing is from 20 Hz to 20,000 Hz

Question 27

What is the Doppler effect? Does the Doppler effect apply to all waves?

Answer 27

The Doppler effect describes the difference between the actual frequency of a wave (including sound), and its perceived frequency when the source of the wave and the wave detector are moving relative to one another. The Doppler effect applies to all waves, including light. If the source of light is moving away from the detector, it is red shifted (decreased frequency). If the source of light is moving toward the detector, it is blue shifted (increase frequency).

Question 28

What are infrasonic waves? What are ultrasonic waves?

Answer 28

Infrasonic waves are sound waves with frequencies below 20 Hz. Ultrasonic waves are sound waves with frequencies above 20,000 Hz.

Question 29

What is the Doppler effect equation?

Answer 29

Question 30

Considering the equation for the Doppler effect, draw it, how do we use the sign convention?

Answer 30

Memorize this form of sign convention. The upper sign should be used when the detector or source is moving toward the other object. The lower sign should be used when the detector or source is moving away from the other object.

Question 31

This is an exercise for sign convention of the Doppler effect equation. Derive the Doppler effect equation for both circumstances: You’re driving down the street and there is an ambulance approaching from behind. You’re driving down the street and the ambulance has passed you and continues to speed down the road.

Answer 31

In these circumstances, you are the detector and the ambulance is the source. In the first circumstance, you (detector) are driving away from the ambulance (source) and the ambulance is driving toward you. In the second circumstance, you are driving toward the ambulance and the ambulance is driving away from you.

Question 32

Let’s drill the sign convention for the Doppler effect one more time. What is the Doppler effect equation? What is the sign convention for the Doppler effect equation?

Answer 32

The way I am remembering the Doppler equation is the detector is more important so it is in the numerator. Toward is top of the signs, away is bottom of signs. Top to bottom goes plus minus minus plus.

Question 33

What is echolocation and how does the Doppler effect play into echolocation?

Answer 33

Echolocation, the animal emitting the sound serves as both the source and the detector of the sound. The sound bounces off the surface and is reflected back to the animal. How long it takes for the sound to return, and the change in frequency of the sound can be used to determine the position of objects in the environment and the speed of which they are moving.

Question 34

Doppler effect example page 260

Answer 34

Work with this so that the answer is intuitive.

Question 35

What is a shockwave, what is a sonic boom, what is Mach 1?

Answer 35

Question 36

What is loudness or volume? How does this relate to sound intensity?

Answer 36

The loudness or volume of a sound is the way in which we perceive its intensity. Perception of loudness or volume is subjective as it depends, not only on brain function, but also physical factors such as obstruction of the air canal, stiffening of the cycle, or damage to the cochlear hairs by exposure to loud noises or with age. Loudness is desire rely related to the waves amplitude. Intensity, however, is objectively measurable. Intensity is the average rate of energy transfer per area across a surface that is perpendicular to the wave.

Question 37

What is sound intensity? How do we calculate sound intensity? What are the units of intensity?

Answer 37

Intensity is the power transported per unit area (average rate of energy transfer per area across a surface that is perpendicular to the wave)

Question 38

What is the relationship of the amplitude of a sound wave and its intensity?

Answer 38

Intensity is proportional to the square of the amplitude. Doubling the amplitude produces a sound wave that has four times the intensity.

Question 39

What is the relationship between intensity and the distance from the source of a sound wave?

Answer 39

Because the surface area of sphere increases as a function of the square of the radius (A=4pir^2), sound waves transmit their power over larger and larger areas the farther from the source they travel. Intensity is inversely proportional to the square of the distance from the source.

Question 40

What is the equation for intensity? What is the relationship of intensity and amplitude? What is the relationship of intensity and distance traveled from source?

Answer 40

Question 41

What is the softest sound that a typical human ear can hear in terms of intensity? What is the highest threshold (threshold of pain)? It would intensity will cause instant perforation of the eardrum? The purpose of this card is to demonstrate the need for logarithmic scales regarding sound intensity.

Answer 41

Question 42

What is the low threshold of intensity for human hearing?

Answer 42

Question 43

The huge range in intensity between the softest sound detectable and eardrum perforation makes a linear scale unmanageable. To make things easier to work with, we use a logarithmic scale, called the sound level (beta) measured in decibels (dB). What is the equation for sound level?

Answer 43

This creates a logarithmic relationship with the ratio of intensity of a given sound wave to the sound wave of minimum intensity detectable by human ears.

Question 44

What are the decibels of the intensity of a sound wave of 10^-12?

Answer 44

This card demonstrates that the decibels are 10 log (I/Io) (10 times the log of the ratio of a given intensity and the lowest detectable sound wave for a human ear (10^-12 W/m^2)). If the given intensity is equal to the low threshold intensity, it will be 10log(1)=0.

Question 45

When the intensity of a sound has changed by some factor, one can calculate the new sound level by using what equation?

Answer 45

Question 46

What is log(1000)? Log(10^8)? Log(10)? Log(1)? Log(.00001)? Log(10^-68)?

Answer 46

Question 47

Recall log for scientific notation. What is the app image value for -log3.5x10^-5?

Answer 47

Question 48

Table of sound levels and relative intensities of several sound sources and thresholds. What is the relationship between decibels and intensity?

Answer 48

An increase in 10 dB is a 10 fold increase in intensity.

Question 49

Sound intensity and decibel example page 263.

Answer 49

This question uses the equation for intensity, shows us how to calculate sound level in decibels, and shows us ratio of intensities given decibels.

Question 50

What is damping (attenuation)? What is the presence of non-conservative forces due to amplitude, intensity, and sound level? Does damping have an effect on the frequency of a wave?

Answer 50

Damping is the decrease in intensity associated with a wave being subject to non-conservative forces in other systems including friction, resistant, and viscous drag. The presence of a non-conservative force causes the system to decrease in amplitude during each oscillation. This will decrease amplitude, intensity, and sound level (loudness), resulting in a loss of sound. Damping does not have an effect on the frequency of a wave, so the pitch will not change.

Question 51

What are beat frequencies? How do we calculate beat frequencies?

Answer 51

Beat frequencies are the wawawa sound when two sounds are slightly different frequencies are produced in proximity.

Question 52

What are closed boundaries and open boundaries? Use examples.

Answer 52

Closed boundaries are those that do not allow oscillation and that correspond to nodes. The closed end of a pipe and the secured end of a string are both considered closed boundaries. Open boundaries are those that allow maximal oscillation and correspond to anti-nodes. The open end of a pipe in the end of a flag are both open boundaries.

Question 53

What is the first second third harmonic of a string closed on both ends? What are the wavelengths in terms of L?

Answer 53

Question 54

Shortcut for determining the harmonic of a string attached at both ends?

Answer 54

The harmonic of a string attached at both ends will be equal to the amount of antinodes on the string.

Question 55

What is the equation that relates the wavelength of a standing wave and the length L of a string that supports it?

Answer 55

Question 56

What is the harmonic of a string attached at both ends?

Answer 56

In the equation that relates the wavelength of a standing wave of a string attached to both ends, n is a positive non-zero integer (n=1,2,3, and so on) call the harmonic. The harmonic corresponds to the number of half wavelengths supported by the string. A shortcut for strings attached at both ends is that the number of antinode present will tell you which harmonic it is.

Question 57

How do you calculate the number of possible frequencies of a string attached two ends?

Answer 57

Question 58

What is the fundamental frequency (first harmonic), what is the first overtone (second harmonic), what is the second overtone (third harmonic) for string attached to both ends? What is the harmonic series?

Answer 58

The lowest frequency, longest wavelength, of a standing wave that can be supported in a given length of string is known as the fundamental frequency (first harmonic). The frequency of the standing wave given by n=2 (two half-wavelength) is known as the first overtone or second harmonic. The frequency of the standing wave given by n=3 (3 half-wavelengths) is known as the second overtone or third harmonic. Harmonic series are all the possible frequencies that the string can support.

Question 59

As a shortcut, how do you determine what the harmonic is of a string attached at both ends?

Answer 59

As a shortcut, for strings attached to both ends, the number of antinode’s present will tell you which harmonic it is. Recall that for an open pipe, it is the number of nodes present that tells us which harmonic it is.

Question 60

What is an open pipe, what is a closed pipe? Give example examples of instruments of each.

Answer 60

Pipes that are open at both ends are called open pipes (flutes are open end instruments. The distal end is open and the mouthpiece on the proximal end is close enough for it to function as an open end) Pipes that are closed at one end and open at the other are called closed pipes. (brass instruments are closed pipe instruments. The proximal end by the musician’s mouth is small enough to be considered a closed end)

Question 61

What is the similarity between harmonics of an open pipe and a string attached to both ends?

Answer 61

The length of the pipe corresponds to 1/2 the wavelength if a standing wave is set up such that there is only one node between the two anti-nodes at the end. This is analogous to a string, except that the ends are both anti-nodes instead of nodes. The second harmonic or first overtone has a wavelength equal to the length of the pipe. The third harmonic, second overtone, has a wavelength equal to 2/3 the length of the pipe.

Question 62

What is the relationship between the wavelength of a standing wave and the length of an open pipe, and the possible frequencies of harmonic series?

Answer 62

It will be the same for a string attached to two ends.

Question 63

What is the shortcut for determining the harmonic for an open pipe?

Answer 63

As a shortcut for open pipes, the number of nodes present will tell you which harmonic it is. Recall that the number of anti-nodes for a string attached to two ends tells us which harmonic it is.

Question 64

When drawing the harmonics of a string attached to both ends, or an open pipe, or a closed pipe, they present to us as transverse waves. Is sound a transverse wave?

Answer 64

The appearance of a transverse wave when we draw them is really a symbolic representation for simplicity. This is a conventional way of diagramming standing waves of sound as drawing longitudinal waves (recalling that sound is a longitudinal wave and not a transverse wave) is more difficult.

Question 65

Draw the first three harmonics of a closed pipe. What is the length and wavelength of the first three harmonics?

Answer 65

Noticed that the fundamental frequency of a closed pipe is 1/4 wavelength. Noticed that n can only be odd integers (n=1,3,5,7…) given the restraint of having one closed end and one open end.

Question 66

What is the equation that relates the wavelength of a standing wave and the length of a closed pipe that supports it?

Answer 66

Question 67

What is the equation for frequency of a standing wave in a closed pipe?

Answer 67

Question 68

How do you determine the harmonic of an closed pipe?

Answer 68

When presented with a closed pipe, count the number of quarter wavelengths contained in the pipe to determine the harmonic.

Question 69

Draw the first second and third harmonic for strings attached on both ends and open pipes and the relevant equations. Draw the first third and fifth harmonic for closed pipe and the relevant equations. Relevant equations are length wavelength and frequency.

Answer 69

Question 70

What is ultrasound?

Answer 70

Ultrasound is high frequency, sound waves outside of the range of human hearing.

Question 71

How are ultrasounds used in medicine?

Answer 71

Ultrasound uses high frequency sound waves outside the range of human hearing to compare the relative densities of tissues in the body. Ultrasound can also be used therapeutically. Ultrasound waves create friction and heat when they act on tissues, which can increase blood flow to a site of injury and deep tissues and promote faster healing. Focused ultrasound can produce constructive interference at a focal point of a mirror creating very high energy waves exactly at a point, which can be used to non-invasively break up kidney stones and ablate (destroy) small tumors. Ultrasound can also be used for dental cleaning and destruction of cataracts.

Question 72

What is lithotripsy? What does ablate mean? What is phacoemulsification?

Answer 72

These are all related to medical applications of ultrasound. Lithotripsy (lith-uh-tripsy) as a procedure to noninvasively break up stones in the urinary tract such as kidney stones. Ablate (uh-blare) means to remove body tissue or to gradually remove material from, erode. Ultrasonic sound can be used to ablate small tumors. Phacoemulsification (fay-cuh) is a surgical procedure to remove cataracts using ultrasound (phaco means lentil, referring to the lens of the eye).

Question 73

In addition to the standard ultrasound, what is Doppler ultrasound?

Answer 73

Doppler ultrasound is used to determine the flow of blood within the body by detecting the frequency shift that is associated with movement toward or away from the receiver.

Question 74

MCAT concept check sound 7.2 page 269 question 1 How is sound produced in transmitted?

Answer 74

Sound is produced by mechanical vibrations. These are usually generated by solid objects, like bells, or vocal cords, but occasionally can be generated by fluids. Sound as propagated as longitudinal waves and matter, so it cannot propagate a vacuum.

Question 75

MCAT concept check sound 7.2 page 269 question 2

Answer 75

The amplitude of a wave is related to its sound level (volume) the frequency of a wave is related to its pitch.

Question 76

MCAT concept check sound 7.2 page 269 question 3

Answer 76

Question 77

MCAT concept check sound 7.2 page 269 question 4 What phenomenon can be detected or treated using ultrasound?

Answer 77

Ultrasound can be used for prenatal screening, or to diagnose gallstones, breast and thyroid masses, and blood clots. It can be used for needle guidance in a biopsy, for dental cleaning, and for treating deep tissue injury, kidney stones, certain, small, tumors, and cataracts, among many other applications.

Question 78

MCAT concept check sound 7.2 page 269 question 5

Answer 78

We need to commit to memory the equation for the wavelength and frequency of strings, closed pipes, and open pipes. There are boxes around those for all three examples in the image.

Question 79

MCAT master chapter 7 waved and sound page 246 question 1

Answer 79

Question 80

MCAT master chapter 7 waved and sound page 246 question 2

Answer 80

This is a good question, understand it.

Question 81

MCAT master chapter 7 waved and sound page 246 question 3

Answer 81

Question 82

MCAT master chapter 7 waved and sound page 246 question 4

Answer 82

Question 83

MCAT master chapter 7 waved and sound page 246 question 5

Answer 83

We need to know that the period is inversely proportional to the frequency, so doubling in frequency would half the period.

Question 84

What is the period of a wave?

Answer 84

The period of a wave is the amount of time it takes a single wave cycle to complete. The period of a wave is the inverse of the frequency (T=1/f)

Question 85

MCAT master chapter 7 waved and sound page 246 question 6

Answer 85

We need to know that the velocity of a wave is equal to the product of frequency and wavelength, and that period is the inverse of frequency. Also, I got stuck on converting 10 cm meters. Do the algebra do the math do the conversion if you’re ever unsure. Conversion shown in blue.

Question 86

MCAT master chapter 7 waved and sound page 246 question 7

Answer 86

For this question, we needed to know n for the third harmonic of a closed pipe. We need to know the equation for the wavelength of a closed pipe. Then we need to know how to calculate the frequency given velocity and wavelength. Then understanding that angular frequency is the product of the frequency and 2pi. Just practice, you’ll get it.

Question 87

MCAT master chapter 7 waved and sound page 246 question 8

Answer 87

We thought this one out and came up with the answer (given multiple choices). We know that a 10 dB increase correlates to a tenfold increase in intensity. It is a good exercise to do this mathematically as shown in the image.

Question 88

MCAT master chapter 7 waved and sound page 246 question 9

Answer 88

Question 89

MCAT master chapter 7 waved and sound page 246 question 10

Answer 89

Question 90

MCAT master chapter 7 waved and sound page 246 question 11

Answer 90

The answer is D. This is a bit of a silly question. This question is testing on the understanding of the Doppler effect. The car must be moving at the same speed as the student than the relative motion between them could be zero. In all other cases, the student in the sound source are necessarily moving relative to each other other.

Question 91

MCAT master chapter 7 waved and sound page 246 question 12

Answer 91

Question 92

MCAT master chapter 7 waved and sound page 246 question 13

Answer 92

Question 93

MCAT master chapter 7 waved and sound page 246 question 14

Answer 93

This is interesting. At first, I thought that it would be the same if the detector was moving towards the stationary source, or the detector was stationary and the source was moving. Apparently, this is not the case. The scenario described in statement, two will produce a similar, but not identical, frequency for the detector. The apparent frequency will increase, but the increase will not be exactly the same as if the detector had been moving. The Doppler effect is different when the source is moving compared to when the detector is moving because when the source moves, it physically compresses or stretches the wavefronts themselves, altering the wavelength of the waves reaching the detector, while when the detector moves, it simply encounters the wavefronts at a different rate, not changing the wave pattern itself; essentially, the relative position of the wavefronts is different in each scenario.

Question 94

MCAT master chapter 7 waved and sound page 246 question 15

Answer 94

Question 95

Relevant equations and relationships for chapter 7 waves and sound

Answer 95