Medical Tests Medical Tests Certifications MCAT-TEST Questions & Answers

• Question 191:

  Aclown stands with her toes touching a fun house mirror with a convex bottom and a concave top. Which of the following best describes the distortion of the clown's image as she walks away from the mirror?

  A. Her head will shrink; her feet will grow, then shrink.

  B. Her head will shrink then grow; her feet will shrink, then grow.

  C. Her head will grow; her feet will grow.

  D. Her head will grow, then shrink; her feet will shrink.

  Correct Answer: D

  Note that we can determine either the convex or concave mirror distortion to answer the question. We do not need to determine both. Solving for the convex bottom, we first note that the focal length of a convex mirror must be some negative value (while for the convex mirror it will be negative). We will solve this problem by drawing a diagram.Let's draw a diagram and examine the distortion of the clown's feet in the convex bottom of the mirror as she walks away from it. Recall that we can draw three kinds of rays in a ray tracing diagram:1.Rays that pass through the focal point will be reflected parallel. For a convex mirror, rays directed towards the focal point will be reflected parallel (because the focal point is in the virtual space behind the mirror).2. Rays that hit the axis of the mirror will be reflected with the same angle on the other side of the axis (like a plane mirror).3. Parallel rays will be reflected through the focal point. For a convex mirror, parallels rays will appear to pass through the focal point (because the focal point is in the virtual space behind the mirror.

  

  The image shrinks as the object moves farther from a convex mirror.

  From the diagram above, it is clear that the image in a convex mirror shrinks as the object moves away. Thus, the image of the clown's feet will shrink in the convex bottom of the mirror as she walks away.

• Question 192:

  The kinetic molecular theory describes gases as composed of randomly moving particles. According to this theory, at constant temperature, the pressure of a gas in a cylinder increases when the volume is decreased because:

  A. the kinetic energy of the gas increases.

  B. the collisions of gas particles with the cylinder become more energetic.

  C. the mass of the particles increases to compensate for the decrease in volume.

  D. the collisions of gas particles with the cylinder increase in frequency.

  Correct Answer: D

  As the volume of the gas decreases, the space between molecules decreases and the frequency of collisions with the cylinder will increase.Choices A and B are incorrect because the kinetic energy is directly related to the temperature of a gas. If the temperature does not change, the kinetic energy will not increase.Choice C is incorrect because the mass of gas particles will not change.

• Question 193:

  Which of the following molecules has the same geometric configuration of electron pairs about the central nucleus as CH4?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: A

  

  The electron pairs in CH4 are arranged in the tetrahedral form typical of sp3 hybridization.

  In water, the electron pairs are also arranged tetrahedrally. This allows maximum separation between electron pairs and gives water its characteristic bent geometry.

  

  Choice B is incorrect. Methanal (formaldehyde) has an sp2 hybridized carbon leading to a planar configuration of constituents.

  

  Choice C is incorrect. BH3 has a trigonal planar configuration of electron pairs (and bonds).

  

  Choice D is incorrect because CO2 has a linear configuration. The C is sp hybridized.

  

• Question 194:

  Musical instruments generate vibrations in the air that are perceived as musical tones. In many kinds of drums, these vibrations are created by a standing waves in a vibrating membrane. In a timpani drum, membrane vibration is coupled to the vibration of an enclosed volume of air. There may also be a second membrane whose vibration is coupled to that of the first by the enclosed air space, as in a snare drum. An idealized circular membrane will vibrate at normal mode frequencies given by Equation 1 where T is the membrane tension, r is the membrane radius, is the mass per unit area of the membrane, and frel is the relative frequency shown under each mode in Figure 1. The pitch of drums can be tuned by adjusting the membrane tension.

  

  Equation 1

  The modes are designated by two numbers, m and n. m indicates the number of diameter nodes, and n indicates the number of circular nodes. Several modes of vibration are shown in Figure 1.

  

  Figure 1

  The speed of sound is inversely proportional to the square root of the density of the gaseous medium through which it travels. Which of the following statements is true regarding an ideal membrane played in a low pressure environment?

  A. The sound intensity will decrease because the vibrations will be more rapidly dispersed.

  B. The vibration of the membrane will occur with greater amplitude at the higher modes.

  C. The pitch will be higher because the frequency of vibration will increase.

  D. The pitch will remain unchanged because the frequency of vibration is not changed.

  Correct Answer: D

  The frequency of vibration of the membrane determines the frequency of pressure waves in the air, and thus, the pitch of the sound detected. Changing the density of the air will not change the frequency of vibration of an ideal membrane. Note that air density does not appear in Equation 1.The wavelength will change as shown by the following equation:Speed of Sound = wavelength ?frequencyIf the speed of sound increases, the wavelength will increase as well, while the frequency remains constant.Choice A is incorrect because the sound intensity at a particular point will not be changed. Sound intensity depends on the distance from the source and the amplitude of the wave, not on the speed of sound in a particular medium.Choice B is incorrect because the amplitude of vibration is not directly related to the medium in which the vibration occurs.Choice C is incorrect because the pitch will not change.

• Question 195:

  Musical instruments generate vibrations in the air that are perceived as musical tones. In many kinds of drums, these vibrations are created by a standing waves in a vibrating membrane. In a timpani drum, membrane vibration is coupled to the vibration of an enclosed volume of air. There may also be a second membrane whose vibration is coupled to that of the first by the enclosed air space, as in a snare drum. An idealized circular membrane will vibrate at normal mode frequencies given by Equation 1 where T is the membrane tension, r is the membrane radius, is the mass per unit area of the membrane, and frel is the relative frequency shown under each mode in Figure 1. The pitch of drums can be tuned by adjusting the membrane tension.

  

  Equation 1

  The modes are designated by two numbers, m and n. m indicates the number of diameter nodes, and n indicates the number of circular nodes. Several modes of vibration are shown in Figure 1.

  

  Figure 1

  The sound waves generated by a drum are:

  A. longitudinal waves because the displacement is perpendicular to the direction of propagation.

  B. longitudinal waves because the displacement is parallel to the direction of propagation.

  C. transverse waves because the displacement is perpendicular to the direction of propagation.

  D. transverse waves because the displacement is parallel to the direction of propagation.

  Correct Answer: B

  Sound waves are longitudinal waves in which pressure displacement occurs parallel to the propagation of the wave. This is in contrast to transverse waves, like those in the ocean, in which the displacement (up and down motion of the water) is perpendicular to the direction of propagation of the wave.

• Question 196:

  Musical instruments generate vibrations in the air that are perceived as musical tones. In many kinds of drums, these vibrations are created by a standing waves in a vibrating membrane. In a timpani drum, membrane vibration is coupled to the vibration of an enclosed volume of air. There may also be a second membrane whose vibration is coupled to that of the first by the enclosed air space, as in a snare drum. An idealized circular membrane will vibrate at normal mode frequencies given by Equation 1 where T is the membrane tension, r is the membrane radius, is the mass per unit area of the membrane, and frel is the relative frequency shown under each mode in Figure 1. The pitch of drums can be tuned by adjusting the membrane tension.

  

  Equation 1

  The modes are designated by two numbers, m and n. m indicates the number of diameter nodes, and n indicates the number of circular nodes. Several modes of vibration are shown in Figure 1.

  

  Figure 1

  Which of the following combinations of modal frequencies would generate the highest beat frequency?

  A. (0,1) and (2,1)

  B. (0,1) and (0,2)

  C. (1,1) and (3,1)

  D. (2,1) and (1,2)

  Correct Answer: B

  Sounds that differ in their frequency produce "beats" of high amplitude by interference at a frequency equal to the difference between their frequencies. The greater the difference in frequencies between the two sounds, the greater will be the frequency of the beats produced. Musicians may use beats to help tune intruments. When an instrument is tuned to a known frequency, the beats will slow down, then disappear when the frequencies are equal.

  

  The relative frequencies given in Figure 1 are directly proportional to the actual frequency of vibration, so we can compare them directly. Among the choices, the greatest difference is between the (0,1) and (0,2) modes.

• Question 197:

  Fireworks have been used for centuries in celebrations around the world. One of the primary components of these devices, black powder, was developed by the Chinese over a thousand years ago and is still used today as a propellant and explosive. Black powder is composed of potassium nitrate (KNO3), charcoal (primarily C) and sulfur (S8) in a 75:15:10 ratio by weight. It is very stable if kept dry but can easily be ignited by a spark or burning fuse to undergo the following reaction:

  

  Reaction 1 The basic firework is shown in Figure 1. Fireworks rely on a particular kind of combustion in which oxygen is supplied by oxidizing agents included in the pyrotechnic mixture. When ignited, the solid propellant begins to liquefy and vaporize allowing the fuel and oxidizing agents to interact more intimately leading to rapid expansion of gases. Delay fuses time the ignition of the other compartments to occur when the shell is high above ground.

  

  Figure 1

  The light generating units of the firework are called stars and are dispersed and ignited by the bursting charge in each compartment. The intense colors of modern fireworks are generated by molecular emitters. For example, barium chloride emits green light (510?30 nm) and strontium chloride emits vibrant red light (605?50 nm). Many of the molecular emitters are unstable at room temperature and so cannot be placed directly into the firework. Instead, they are synthesized in the flame of the pyrotechnic reaction and exist for a short time before decomposing. The flame temperature must be carefully adjusted so that these emitters do not decompose too rapidly.

  

  What is the energy of a photon of light emitted by a barium chloride emitter?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: B

  In order to determine the energy of a photon, we plug the value of the frequency emitted into the equation:

  E = hf

  Note that if you did not remember this equation, you could use the constants provided at the bottom of the passage to determine the equation through dimensional analysis. Energy has units of J, so multiplying a s-1 value by h would provide a

  calculation of energy.

  The passage provides the wavelength of light produced by barium chloride as 510--530 nm. We can perform the calculation with the approximate value of 500 nm.

  

• Question 198:

  Musical instruments generate vibrations in the air that are perceived as musical tones. In many kinds of drums, these vibrations are created by a standing waves in a vibrating membrane. In a timpani drum, membrane vibration is coupled to the vibration of an enclosed volume of air. There may also be a second membrane whose vibration is coupled to that of the first by the enclosed air space, as in a snare drum. An idealized circular membrane will vibrate at normal mode frequencies given by Equation 1 where T is the membrane tension, r is the membrane radius, is the mass per unit area of the membrane, and frel is the relative frequency shown under each mode in Figure 1. The pitch of drums can be tuned by adjusting the membrane tension.

  

  Equation 1

  The modes are designated by two numbers, m and n. m indicates the number of diameter nodes, and n indicates the number of circular nodes. Several modes of vibration are shown in Figure 1.

  

  Figure 1

  If the tension of a drum membrane is increased by a factor of four and the radius is increased by a factor of two, then the (1,1) modal frequency would:

  A. not change.

  B. increase by a factor of 1.59.

  C. increase by a factor of 2.

  D. increase by a factor of 4.

  Correct Answer: A

  Looking at Equation 1, we see that the frequency is inversely proportional to the membrane radius and directly proportional to the square root of the tension.

  

  inversely proportional to membrane radius directly proportional to square root of membrane tension

• Question 199:

  Musical instruments generate vibrations in the air that are perceived as musical tones. In many kinds of drums, these vibrations are created by a standing waves in a vibrating membrane. In a timpani drum, membrane vibration is coupled to the vibration of an enclosed volume of air. There may also be a second membrane whose vibration is coupled to that of the first by the enclosed air space, as in a snare drum. An idealized circular membrane will vibrate at normal mode frequencies given by Equation 1 where T is the membrane tension, r is the membrane radius, is the mass per unit area of the membrane, and frel is the relative frequency shown under each mode in Figure 1. The pitch of drums can be tuned by adjusting the membrane tension.

  

  Equation 1

  The modes are designated by two numbers, m and n. m indicates the number of diameter nodes, and n indicates the number of circular nodes. Several modes of vibration are shown in Figure 1.

  

  Figure 1

  Chladni patterns are formed when fine sand is placed on a vibrating membrane. The regions of localized sand indicate the:

  A. circular nodes only.

  B. antinodes.

  C. circular nodes and diameter nodes.

  D. region equidistant between nodes and antinodes.

  Correct Answer: C

  The nodes of a standing wave are the points where the amplitude is zero, the static points. In a drum membrane, these are regions where there is no motion of the membrane. As the adjacent membrane regions vibrate, sand will accumulate at the points where no vibration occurs (nodes: either circular or diameter), forming the Chladni patterns.Choice A is incorrect because sand would accumulate at both the circular and diameter nodes. Choice B is incorrect because the antinodes are the points of maximum amplitude where sand would be least likely to stay.Choice D is incorrect because the point between the nodes and antinodes would vibrate.

• Question 200:

  Fireworks have been used for centuries in celebrations around the world. One of the primary components of these devices, black powder, was developed by the Chinese over a thousand years ago and is still used today as a propellant and explosive. Black powder is composed of potassium nitrate (KNO3), charcoal (primarily C) and sulfur (S8) in a 75:15:10 ratio by weight. It is very stable if kept dry but can easily be ignited by a spark or burning fuse to undergo the following reaction: Reaction 1 The basic firework is shown in Figure 1. Fireworks rely on a particular kind of combustion in which oxygen is supplied by oxidizing agents included in the pyrotechnic mixture. When ignited, the solid propellant begins to liquefy and vaporize allowing the fuel and oxidizing agents to interact more intimately leading to rapid expansion of gases. Delay fuses time the ignition of the other compartments to occur when the shell is high above ground.

  

  

  Figure 1

  The light generating units of the firework are called stars and are dispersed and ignited by the bursting charge in each compartment. The intense colors of modern fireworks are generated by molecular emitters. For example, barium chloride emits green light (510?30 nm) and strontium chloride emits vibrant red light (605?50 nm). Many of the molecular emitters are unstable at room temperature and so cannot be placed directly into the firework. Instead, they are synthesized in the flame of the pyrotechnic reaction and exist for a short time before decomposing. The flame temperature must be carefully adjusted so that these emitters do not decompose too rapidly.

  

  Flares, a particular kind of pyrotechnic device, can burn underwater. Most materials, like wood, cannot burn underwater. Which of the following provides the best explanation for this difference?

  A. The combustion of wood has a lower H.

  B. Flares have a lower ignition temperature and can be easily ignited by a spark or fuse.

  C. Combustion of wood requires oxygen which is not provided by water.

  D. Water is a powerful flame retardant that extinguishes flames by increasing the activation energy of combustion.

  Correct Answer: C

  In most combustion reactions, oxygen is provided by the air. Flares can burn underwater because the pyrotechnic combustion mixture includes an oxidizing agent. In black powder, KNO3 is the oxidizing agent.Choice A is incorrect because H is a measure of the enthalpy change of a reaction which indicates if heat is released or absorbed by the reaction. Both burning wood and burning flares are exothermic. The degree of exothermicity is not relevant to burning without an outside oxygen source. Choice B is incorrect because wood can be ignited by a spark. Again, the activation energy of the reaction is not relevant to burning underwater. Choice D is incorrect: water is a powerful flame retardant because it suffocates a flame by decreasing oxygen supply. Water does not increase the activation energy of combustion.