AP Physics - Problem Drill 11: Vibrations and Waves. Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as 1. The following definitions are used to describe the oscillatory motion of a body. Identify what is being defined in each of these statements. (1) The distance from the equilibrium point to the body at an instant in time. (2) The maximum displacement from the equilibrium point. (3) The time to move through one complete cycle, or oscillation. (4) The number of oscillations per unit of time. (A) displacement, (2) period, (3) frequency, (4) amplitude (B) displacement, (2) amplitude (3) speed (4) period (C) displacement, (2) amplitude (3) period (4) frequency (D) amplitude (2) period (3) frequency (4) speed (E) amplitude (2) displacement (3) frequency (4) period Check the definition for period. Check the definition for speed. C. Correct! Start with the displacement of the oscillatory motion, then amplitude, period, and finally frequency. D. Incorrect! Check the definition of frequency. Review all the terms used to describe oscillatory motion. Displacement: The distance from the equilibrium point to the body at any instant in time. Amplitude: The maximum displacement from the equilibrium point. Period: The time to move through one complete cycle, or oscillation. Frequency: The number of oscillations per unit of time. The correct answer is (C).
No. 2 of 10 2. Which of these statements does not describe a simple harmonic oscillator? (A) A vibrating system in which the restoring force is directly proportional to the negative of the displacement. (B) A mass that vibrates at its natural frequency on the free end of a spring. (C) The pendulum of a grandfather clock. (D) A vibrating system whose period of oscillation depends on the amplitude of the oscillation. (E) A vibrating system whose period of oscillation is proportional to the square root of the mass of the system. A simple harmonic oscillator is a vibrating system that obeys the equation F= -kx. Where F is force, k is a force constant, and x is displacement. The negative sign indicates that it is a restorative force, meaning that the force acts to bring the system back to the equilibrium position. A mass on a spring follows the equation F= -kx. Where F is force, k is a force constant, and x is displacement. A pendulum is one of the examples that are typically given. Provided that the angle over which it swings is not too large the pendulum will move in SHM. The period of oscillation for a system in simple harmonic motion is given by the m equation T 2, where m is mass, k is force constant. There is no term for k amplitude. The period of oscillation for a system in simple harmonic motion is given by the m equation T 2, where m is mass, k is force constant. k A simple harmonic oscillator is a vibrating system that obeys the equation F= -kx. Where F is force, k is a force constant, and x is displacement. The negative sign indicates that it is a restorative force, meaning that the force acts to bring the system back to the equilibrium position. A mass on a spring follows the equation F= -kx. A pendulum is one of the examples that are typically given. Provided that the angle over which it swings is not too large the pendulum will move in SHM. The period of oscillation for a system in simple harmonic motion is given by the m equation T 2, where m is mass, k is force constant. There is no term for k amplitude.
No. 3 of 10 3. Five stationary pendulums are suspended from a single line, the ends of which are tied to supports. The pendulum on the far right is set into motion. Which pendulum vibrates with the largest amplitude? A B C D Drive (A) All the pendulums will vibrate with the same amplitude as the drive pendulum. (B) Pendulum D will vibrate with the highest amplitude. (C) It depends on the mass of the drive pendulum. (D) Pendulum A (E) Pendulum A and D All the pendulums will be set into motion, but the question asks which has the largest amplitude. The drive pendulum will vibrate at its natural frequency. What does the natural frequency of each pendulum depend on? l The period, of a pendulum does not depend on its mass. Remember, T 2, g where l is length of the pendulum and g is acceleration due to gravity. Pendulum A has the same length so will have the same natural frequency as the drive pendulum; this will result in resonance and a rapid transfer of energy and large amplitude. Since has the same length of pendulum A is the same as the drive pendulum l and T 2, they will both have the same natural frequency. g Pendulum A is the same length as the drive pendulum, so they will have the same natural frequency; this will result in resonance and a rapid transfer of energy and large amplitude for pendulum A. The period, of a pendulum does not depend on its mass. Remember, l T 2, g where l is length of the pendulum and g is acceleration due to gravity. Frequency is 1/T.
No. 4 of 10 4. Which of these is incorrect statement about mechanical waves? (A) The ripples generated when a pebble is thrown into a pond are an example of mechanical waves. (B) A medium is any material through which a mechanical wave travels. (C) In a longitudinal wave the direction of propagation of the wave and the direction of the particle vibration are the same. (D) In a transverse wave the particle vibration in a direction parallel to the direction of propagation of the wave. (E) The sound waves created when a drum is beaten are an example of a longitudinal wave. A mechanical wave is a disturbance that travels through a medium. In this case the medium is water. The medium is any material that a mechanical wave travels through; for example air, water, or even your body. For a longitudinal wave the particles in the medium will vibrate in the same direction (parallel) to the direction in which the wave is travelling. For a transverse wave the particles in the medium will vibrate in a direction perpendicular to the direction in which the wave is travelling. Sound waves are longitudinal waves. A mechanical wave is a disturbance that travels through a medium. The medium is any material that a wave travels through, for example air, water, or even your body. For a longitudinal wave the particles in the medium will vibrate in the same direction (parallel) to the direction in which the wave is travelling. Sound waves are longitudinal waves. For a transverse wave the particles in the medium will vibrate in a direction perpendicular to the direction in which the wave is travelling.
No. 5 of 10 5. Which of these distances would be the wavelength of the wave shown? A C (A) A (B) B (C) C (D) All of them (E) None of them B Wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave. Wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave. Wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave. Wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave. Typically the wavelength is illustrated as the distance between two successive peaks or two successive troughs; in fact the wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave. Typically the wavelength is illustrated as the distance between two successive peaks or two successive troughs; in fact the wavelength is the distance between any two successive points that are in identical positions (in phase) on the wave.
No. 6 of 10 6. Two transverse waves on identical strings have frequencies in a ratio of 3 to 2. If their wave speeds are the same, then how do their wavelengths compare? (A) 3:2 (B) 2:3 (C) 9:2 (D) 2:9 (E) 1:6 Frequency and wavelength are not directly proportional. B. Correct Frequency and wavelength are inversely proportional to each other. The wave with the greatest frequency has the shortest wavelength. The wave equation can be used to find the relationship between, speed, frequency and wavelength. D. Incorrect! The wave equation can be used to find the relationship between, speed, frequency and wavelength. The wave equation can be used to find the relationship between, speed, frequency and wavelength The wave equation states that wave speed (v) is equal to the wavelength (λ) times the frequency, (f). v = λf This equation can be rearranged to find the relationship between wavelength and speed and frequency v λ = f So wavelength is inversely proportional to frequency. If the speed is the same for the two waves, which ever wave has the smallest frequency will have the largest wavelength. The ratio will swap. The correct answer is (B).
No. 7 of 10 Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 7. The picture shows a wave pulse travelling back down a rope after it has been reflected. Which of these shows the incident waves for (1) Fixed end reflection (2) Free end reflection? A. 1 2 Air Wall B. 1 2 (1) Fixed end reflection C. 1 2 (2) Free end reflection D. 1 2 E. Insufficient information. A wave that is reflected from a fixed end boundary does not behave in the same way as one reflected from a free end. For a free end reflection the direction of the displacement does not change. For a free end reflection the direction of the displacement does not change. When an incident wave is reflected at boundary that is more dense than the medium it has been travelling in. A wave that is reflected from a fixed end boundary does not behave in the same way as one reflected from a free end. When an incident wave is reflected at a fixed boundary, which is made of a denser medium than the medium the incident wave is travelling through, the reflected wave is inverted. If a crest is incident then the reflection is a trough. When an incident wave is reflected at a free end, or at a medium that is less dense than the medium the incident wave is travelling through, the displacement of the reflected wave is the same as the incident wave. If a crest is incident it is reflected as a crest. Answer: D. 1 2
No. 8 of 10 8. What will happen when two waves pass through the same region of a medium at the same time? (A) They interfere. (B) The resultant displacement at any point and time is the sum of the individual displacements at that point and time. (C) The principle of wave superstition is in effect. (D) Both A and B but not C. (E) A, B and C. Review all the statements. Review all the statements. Review all the statements. D. Incorrect! Review the definition of superposition. E. Correct! Two waves will interfere. The principle of wave superposition is that when two or more waves interfere, the resultant displacement will be the sum of the displacements of the individual waves. Two waves will interfere. The principle of wave superposition is that when two or more waves interfere, the resultant displacement will be the sum of the displacements of the individual waves. When adding the displacements, a crest is considered to be positive and a trough negative. The correct answer is (E).
No. 9 of 10 9. The picture shows how the displacement of two waves changes as a function of time. If these two waves interfere, which of these represents the resultant wave? t=0 1 2 3 A. B. C. D. t=0 1 2 3 E. For constructive interference the waves must be completely in phase. For destructive interference the waves must be completely out of phase. The waves will interfere; use the principle of wave superposition. These waves are out of phase by ¼ of a cycle. There is constructive and destructive interference, the maximum displacement occurs when the waves cross. In this case the resultant amplitude will be greater than the amplitude of the individual waves. The two waves are out of phase by ¼ of a cycle. There will be constructive and destructive interference. The maximum displacement occurs where the two waves cross over. This is best seen by drawing the waves on the same graph, as shown and using the principle of superposition. t=0 1 2 3
No. 10 of 10 10. Which of these is not a characteristic of a standing (stationary) wave created by two travelling waves? (A) The point of minimum displacement is an antinode. (B) The two travelling waves must have the same frequency and amplitude. (C) At a node the standing wave has no displacement. (D) The amplitude of the standing wave is twice that of the two waves. (E) The standing wave has the same wavelength as travelling waves. A. Correct! A node is the point of minimum displacement. An antinode is a point of maximum displacement. To produce a standing wave the two travelling waves would have to have both the same frequency and amplitude. A node is the point of minimum displacement. D. Incorrect! The amplitude of the standing wave is twice that of the two waves. This is the principle of wave superposition. A standing wave will have the same wavelength as the travelling wave. A standing wave will be created by two travelling waves that are moving in opposite directions and have the same amplitude, and frequency. The resulting standing wave will have amplitude that is twice that of the travelling waves. The standing wave will have points of minimum displacement, which are called nodes and maximum displacement called antinodes. The position of these nodes and antinodes do not change over time, hence the name standing or stationary wave. The correct answer is (A).