physics final
The general differential equation that governs the travel of waves of all types is
((∂^(2)y)/(∂x^(2)))=(1/v^2)((∂^(2)y)/(∂t^2)) Here the waves travel along an x axis and oscillate parallel to the y axis, and they move with speed v, in either the positive x direction or the negative x direction.
matter waves
Although these waves are commonly used in modern technology, they are probably very unfamiliar to you. These waves are associated with electrons, protons, and other fundamental particles, and even atoms and molecules. Because we commonly think of these particles as constituting matter, such waves are called matter waves.
If the damping constant is small (b<<sqrt(km)), then ω'≈ω, where ω is the angular frequency of the undamped oscillator. for small b, the mechanical energy ER of the oscillator is given by
E(t)≈(1/2)kx^(2)_me^(-bt/m)
Consider a wire under tension that is driven by an oscillator. Initially, the wire is vibrating in its second harmonic mode. How does the oscillation of the wire change as the frequency is slowly increased? a) No standing wave may be observed until the frequency matches the third harmonic mode of the wire. b) No standing wave may be observed until the frequency matches the first harmonic mode of the wire. c) The observed oscillation of the wire not change until the frequency matches the third harmonic mode of the wire. d) The observed oscillation of the wire will slowly change in fractions of the harmonic between the second and third harmonic modes. e) The observed oscillation of the wire will slowly change in fractions of the harmonic between the second and first harmonic modes.
a) No standing wave may be observed until the frequency matches the third harmonic mode of the wire.
Which one of the following statements concerning the elastic potential energy of a ball attached to a spring is false when the ball is moving in simple harmonic motion? a) The elastic potential energy is at its minimum when the spring is in its equilibrium position. b) The elastic potential energy is smaller when the ball is at x than when it is at +x. c) The elastic potential energy can be expressed in units of watts. d) The elastic potential energy is at its maximum when the velocity of the ball is a maximum. e) The elastic potential energy is at its minimum when the acceleration of the ball is a maximum.
a) The elastic potential energy is at its minimum when the spring is in its equilibrium position.
A block is hung vertically at the end of a spring A block is hung vertically at the end of a spring. When the block is displaced and released, it moves in simple harmonic motion. Which one of the following statements is true concerning the block? a) The maximum acceleration of the block occurs when its velocity is zero. b) The velocity of the block is never zero m/s. c) If the velocity of the block is zero m/s, it acceleration is zero m/s2. d) The maximum velocity occurs when the maximum acceleration occurs.
a) The maximum acceleration of the block occurs when its velocity is zero.
Which one of the following statements correctly describes the wave given as this equation:, where distances are measured in cm and time is measured in ms? a) The wave is traveling in the +x direction with an amplitude of 3 cm and a wavelength of π/2 cm. b) The wave is traveling in the +x direction with an amplitude of -4 cm and a wavelength of π cm. c) The wave is traveling in the +x direction with an amplitude of 3 cm and a wavelength of π cm. d) The wave is traveling in the +x direction with an amplitude of 2 cm and a wavelength of π cm. e) The wave is traveling in the +x direction with an amplitude of 6 cm and a wavelength of π/2 cm.
a) The wave is traveling in the +x direction with an amplitude of 3 cm and a wavelength of π/2 cm.
A radio station broadcasts its radio signal at a frequency of MHz. The signals travel radially outward from a tower at the speed of light. Which one of the following equations represents this wave if t is expressed in seconds and x is expressed in meters? a) y = 150 sin[(6.377 * 108)t - (2.123)x] b) y = 150 sin[(637.7)t - (2.961)x] c) y = 150 sin[(6.283 * 106)t - (2.961 * 103)x] d) y = 150 sin[(101.5 * 106)t - (2.961)x] e) y = 150 sin[(101.5 * 106)t - (2.123)x]
a) y = 150 sin[(6.377 * 108)t - (2.123)x]
Two sinusoidal waves on the same string exhibit interference,
adding or canceling according to the principle of superposition.
Transverse mechanical waves, like those on a stretched string,
are waves in which the particles of the medium oscillate perpendicular to the wave's direction of travel.
How is period (T) related to frequency?
T=1/f
A torsion pendulum consists of an object suspended on a wire. When the wire is twisted and then released, the object oscillates in angular simple harmonic motion with a period given by
T=2π(sqrt(I/k)) where I is the rotational inertia of the object about the axis of rotation and κ is the torsion constant of the wire.
A simple pendulum consists of a rod of negligible mass that pivots about its upper end, with a particle (the bob) attached at its lower end. If the rod swings through only small angles, its motion is approximately simple harmonic motion with a period given by
T=2π(sqrt(I/mgL)) (simple pendulum) where I is the particle's rotational inertia about the pivot, m is the particle's mass, and L is the rod's length.
A physical pendulum has a more complicated distribution of mass. For small angles of swinging, its motion is simple harmonic motion with a period given by
T=2π(sqrt(I/mgh)) (physical pendulum) where I is the pendulum's rotational inertia about the pivot, m is the pendulum's mass, and h is the distance between the pivot and the pendulum's center of mass.
Two waves are traveling along a string Two waves are traveling along a string. The graph shows the position of the waves at time t = 0.0 s. One wave with a maximum amplitude of 0.5 cm is traveling toward the right at 0.5 cm/s. The second wave with a maximum amplitude of 2.0 cm is traveling toward the left at 2.0 cm/s. At what elapsed time will the two waves completely overlap and what will the maximum amplitude be at that time? a) 2.0 s, 1.5 cm b) 1.3 s, 2.5 cm c) 1.0 s, 1.5 cm d) 1.0 s, 2.5 cm e) 1.3 s, 0.0 cm
b) 1.3 s, 2.5 cm
During a rock concert, the lead guitarist plucks the high E (329.6 Hz) string, which has a mass of g and a length of m. The tension on the string is 226 N. If the amplitude of the wave on the string is 3.0 mm, what is the average rate of energy transport on the string? a) 2130 W b) 1760 W c) 975 W d) 547 W e) 122 W
b) 1760 W
Jimmy and Jenny are floating on a quiet river using giant doughnut-shaped tubes. At one point, they are 5.0 m apart when a speed boat passes. After the boat passes, they begin bobbing up and down at a frequency of 0.25 Hz. Just as Jenny reaches her highest level, Jimmy is at his lowest level. As it happens, Jenny and Jimmy are always within one wavelength. What is the speed of these waves? a) 1.3 m/s b) 2.5 m/s c) 3.8 m/s d) 5.0 m/s e) 7.5 m/s
b) 2.5 m/s
What is the period of a simple pendulum consisting of a ball suspended from a 2.0-m string? a) 2.0 s b) 2.8 s c) 3.6 s d) 4.4 s e) 5.2 s
b) 2.8 s
Which one of the following statements concerning simple harmonic motion is false? a) The displacement versus time graph for an object in simple harmonic motion resembles the sine or cosine function. b) A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement. c) The amplitude of the object in simple harmonic motion is the maximum distance the object moves from its equilibrium position. d) During simple harmonic motion, the net force on the object is zero newtons when it is at its equilibrium position. e) A restoring force acts on the object that is proportional to the object's displacement from its equilibrium position.
b) A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement.
An object that obeys Hooke's law is displaced a distance x by a net force F. Which one of the following statements correctly describes the resulting acceleration of the object? a) The magnitude of the acceleration is constant. b) The acceleration increases as x increases and it decreases as x decreases. c) The acceleration is always in the positive x direction. d) The acceleration is only dependent on the mass of the object.
b) The acceleration increases as x increases and it decreases as x decreases.
A climbing rope is hanging from the ceiling in a gymnasium A climbing rope is hanging from the ceiling in a gymnasium. A student grabs the end of the rope and begins moving it back and forth with a constant amplitude and frequency. A transverse wave moves up the rope. Which of the following statements describing the speed of the wave is true? a) The speed of the wave decreases as it moves upward. b) The speed of the wave increases as it moves upward. c) The speed of the wave is constant as it moves upward. d) The speed of the wave does not depend on the mass of the rope. e) The speed of the wave depends on its amplitude.
b) The speed of the wave increases as it moves upward.
Which one of the following correctly describes a wave described by y = 2.0 sin(3.0x - 2.0t) where y and x are measured in meters and t is measured in seconds? a) The wave is traveling in the +x direction with a frequency 6π Hz and a wavelength 3π m. b) The wave is traveling in the -x direction with a frequency 4π Hz and a wavelength π/3 m. c) The wave is traveling in the +x direction with a frequency π Hz and a wavelength 3π m. d) The wave is traveling in the -x direction with a frequency 4π Hz and a wavelength π m. e) The wave is traveling in the +x direction with a frequency 6π Hz and a wavelength π/3 m.
b) The wave is traveling in the -x direction with a frequency 4π Hz and a wavelength π/3 m.
What type of motion is represented by the graph shown? a) simple harmonic motion b) damped harmonic motion c) special harmonic motion d) squeezed harmonic motion e) depleted harmonic motion
b) damped harmonic motion
Complete the following sentence: In harmonic motion, resonance occurs when a) the energy in the system is proportional to the square of the motion's amplitude. b) the driving frequency is the same as the natural frequency of the system. c) the energy in the system is a minimum. d) the system is damped. e) the driving frequency is varying.
b) the driving frequency is the same as the natural frequency of the system.
Which one of the following waves would undergo fully constructive interference with a wave described by y = 2.0 sin (3.0x - 2.0t) where y and x are measured in meters and t is measured in seconds? a) y = sin (0.33x - 0.5t) b) y = - sin (-3.0x + 2.0t) c) y = - sin (-1.5x - t)) d) y = sin (x + 2t/3) e) None of these equations will fully interfere constructively with the given wave.
b) y = - sin (-3.0x + 2.0t)
The equation for a certain wave is y = 4.0 sin [2(2.5t x)] where y and x are measured in meters and t is measured in seconds. What is the magnitude and direction of the velocity of this wave? a) 1.8 m/s in the +x direction b) 1.8 m/s in the -x direction c) 18 m/s in the -x direction d) 7.2 m/s in the +x direction e) m/s in the -x direction
c) 18 m/s in the -x direction
Consider the graph shown for the position of a ball attached to a spring as it oscillates in simple harmonic motion. At which of the following times does the ball have its greatest speed? a) 1 s b) 2 s c) 4 s d) 6 s e) both 2 s and 6 s
c) 4 s
A longitudinal wave with an amplitude of 0 A longitudinal wave with an amplitude of 0.02 m moves horizontally along a Slinky with a speed of 2 m/s. Which one of the following statements concerning this wave is true? a) Each particle in the Slinky moves a distance of 2 m each second. b) Each particle in the Slinky moves a vertical distance of 0.04 m during each period of the wave. c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave. d) Each particle in the Slinky moves a vertical distance of 0.02 m during each period of the wave. e) Each particle in the Slinky has a wavelength of 0.04 m.
c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave.
A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of length L. The ball is displaced from its equilibrium position by a small angle θ and released. Which one of the following statements concerning this situation is correct? a) If the mass were increased, the period of the pendulum would increase. b) The frequency of the pendulum does not depend on the acceleration due to gravity. c) If the length of the pendulum were increased, the angular frequency of the pendulum would decrease. d) The period of the pendulum does not depend on the length of the pendulum. e) The angular frequency would double if the angle θ were doubled.
c) If the length of the pendulum were increased, the angular frequency of the pendulum would decrease.
Mike is holding one end of a Slinky. His hand moves up and down and causes a transverse wave to travel along the Slinky away from him. Is the motion of Mike's hand a wave? a) Yes, the motion of Mike's hand is a wave because it moves up and down in periodic motion. b) Yes, the motion of Mike's hand is a wave because Mike is transferring energy to the Slinky. c) No, the motion of Mike's hand is not a wave because there is no traveling disturbance. d) No, the motion of Mike's hand is not a wave because there is no energy traveling along the Slinky.
c) No, the motion of Mike's hand is not a wave because there is no traveling disturbance.
Simple harmonic motion
corresponds to the projection of uniform circular motion onto a diameter of the circle.
The graph shows two waves at time t = 0 s, one moving toward the right at 2.0 cm/s and the other moving toward the left at 2.0 cm/s. What will the amplitude be at x = 0 at time t = 0.5 s? a) +1 cm b) zero cm c) -1 cm d) -2 cm e) -3 cm
d) -2 cm
A wave is described by the equation y = sin (3.0x 6.0t), where the distances are in meters and time is measured in seconds. Using the wave equation, determine the speed of this wave? a) .50 m/s b) .75 m/s c) 1.0 m/s d) 2.0 m/s e) 4.0 m/s
d) 2.0 m/s
When a wire under tension oscillates in its third harmonic mode, how many wavelengths are observed? a) 1/3 b) 1/2 c) 2/3 d) 3/2 e) 2
d) 3/2
A simple pendulum that swings through a very large angle is not in simple harmonic motion because of which of the following reasons? a) The restoring force depends on the sine of the angle. b) The component of the gravitational force that acts as the restoring force is only linear if the maximum angle is small. c) The angular acceleration does not vary linearly with the angle. d) All of the above reasons are valid explanations.
d) All of the above reasons are valid explanations.
The projection of the rotating phasor on a vertical axis gives the
displacement y of a point along the wave's travel.
Which one of the following waves would undergo fully destructive interference with a wave described by y = 2.0 sin (3.0x - 0.5t) where y and x are measured in meters and t is measured in seconds? a) y = -2.0 sin (3.0x -0.5t) b) y = 2.0 sin (3.0x + 0.5t)) c) y = 2.0 sin (-3.0x - 0.5t)) d) y = 2.0 sin (0.33x - 2.0t) e) None of these equations will fully interfere destructively with the given wave.
e) None of these equations will fully interfere destructively with the given wave.
What is the difference between periodic motion and simple harmonic motion? a) Periodic motion only happens for short periods of time and simple harmonic motion happens continually. b) In periodic motion, the frequency of the motion is continually changing, but in simple harmonic motion, the frequency is constant. c) In periodic motion, the period of the motion is continually changing, but in simple harmonic motion, the period is constant. d) In periodic motion, the amplitude varies with time, but in simple harmonic motion, the position of the object varies with time. e) Periodic and simple harmonic motion refer to the same type of motion.
e) Periodic and simple harmonic motion refer to the same type of motion.
A block of mass M is attached to one end of a spring that has a spring constant k. The other end of the spring is attached to a wall. The block is free to slide on a frictionless floor. The block is displaced from the position where the spring is neither stretched nor compressed and released. It is observed to oscillate with a frequency f. Which one of the following statements is true concerning the motion of the block? a) The block's acceleration is constant. b) The period of its motion depends on its amplitude. c) The block's acceleration is greatest when the spring returns to its equilibrium position. d) The block's velocity is greatest when it reaches its maximum displacement. e) The block's acceleration is greatest when the mass has reached its maximum displacement.
e) The block's acceleration is greatest when the mass has reached its maximum displacement.
An object is in simple harmonic motion. The rate at which the object oscillates may be described using the period T, the frequency f, and the angular frequency . If the angular frequency decreases, what is the effect on the period and the frequency? a) The frequency would decrease, but the period would remain the same. b) The period would increase, but the frequency would remain the same. c) Both the period and the frequency would decrease. d) Both the period and the frequency would increase. e) The period would increase, but the frequency would decrease
e) The period would increase, but the frequency would decrease
Consider the graph shown for the position of a ball attached to a spring as it oscillates in simple harmonic motion. At which of the following times is the ball at its equilibrium position? a) 0 s only b) 2 s only c) 4 s only d) at 0 s and 8 s e) at 0 s, 4 s, and 8 s
e) at 0 s, 4 s, and 8 s
Consider the graph shown for the position of a ball attached to a spring as it oscillates in simple harmonic motion. At which of the following times does the ball have its greatest acceleration? a) 1 s b) 2 s c) 4 s d) 6 s e) both 2 s and 6 s
e) both 2 s and 6 s
A ball is attached to a vertical spring A ball is attached to a vertical spring. The ball is initially supported at a height y so that the spring is neither stretched nor compressed. The ball is then released from rest and it falls to a height y h before moving upward. Consider the following quantities: translational kinetic energy, gravitational potential energy, elastic potential energy. When the ball was at a height y (h/2), which of the listed quantities has values other than zero joules? a) translational kinetic energy only b) gravitational potential energy only c) elastic potential energy only d) translational and elastic potential energies only e) translational kinetic, gravitational potential, and elastic potential energies
e) translational kinetic, gravitational potential, and elastic potential energies
Standing waves are characterized by
fixed locations of zero displacement called nodes and fixed locations of maximum displacement called antinodes.
The frequency f of periodic, or oscillatory, motion is, in the SI system, it is measured in
hertz: 1 Hz = 1/s = 1 s^(-1)
The mechanical energy E in a real oscillating system decreases during the oscillations because external forces, such as a drag force,
inhibit the oscillations and transfer mechanical energy to thermal energy. The real oscillator and its motion are then said to be damped.
The wavelength λ is related to k by
k=2π/λ
electromagnetic waves
These waves are less familiar, but you use them constantly; common examples include visible and ultraviolet light, radio and television waves, microwaves, x rays, and radar waves. These waves require no material medium to exist. Light waves from stars, for example, travel through the vacuum of space to reach us. All electromagnetic waves travel through a vacuum at the same speed c=299792458 m/s
Mechanical waves.
These waves are most familiar because we encounter them almost constantly; common examples include water waves, sound waves, and seismic waves. All these waves have two central features: They are governed by Newton's laws, and they can exist only within a material medium, such as water, air, and rock.
A wave is described by the equation y = 0. 25 sin (kx 4 A wave is described by the equation y = 0.25 sin (kx 4.0t), where the distances are in meters and time is measured in seconds. The wave is moving along a string under tension at a speed of 0.75 m/s. Using the wave equation, determine the value of k? a) 5.3 m^-1 b) 1.0 m^-1 c) .19 m^-1 d) .75 m^-1 e) 1.3 m^-1
a) 5.3 m^-1
The drawing shows the vertical position of points along a string versus distance as a wave travels along the string. Six points on the wave are labeled A, B, C, D, E, and F. Between which two points is the length of the segment equal to one wavelength? a) A to E b) B to D c) A to C d) A to F e) C to F
a) A to E
A block of mass M is attached to one end of a spring that has a spring constant k. The other end of the spring is attached to a wall. The block is free to slide on a frictionless floor. The block is displaced from the position where the spring is neither stretched nor compressed and released. It is observed to oscillate with a frequency f. Which one of the following actions would increase the frequency of the motion? a) Decrease the mass of the block. b) Increase the length of the spring. c) Reduce the spring constant. d) Reduce the distance that the spring is initially stretched. e) Increase the distance that the spring is initially stretched.
a) Decrease the mass of the block.
A ball of mass m is attached to the end of a spring with a spring constant k. When the ball is displaced from its equilibrium position and released, it moves in simple harmonic motion. Consider the relationship between the angular frequency, the mass, and the spring constant given in the text. Which one of the following statements concerning that relationship is true? a) Increasing the spring constant causes the angular frequency to increase. b) Increasing the mass of the ball causes the angular frequency to increase. c) Increasing the initial displacement before releasing the ball causes the angular frequency to increase. d) Increasing the period of the ball's motion causes the angular frequency to increase.
a) Increasing the spring constant causes the angular frequency to increase.
A wave can be represented with a
phasor
The speed of a wave on a stretched string is set by
properties of the string, not properties of the wave such as frequency or amplitude.
Standing waves on a string can be set up by
reflection of traveling waves from the ends of the string. If an end is fixed, it must be the position of a node. This limits the frequencies at which standing waves will occur on a given string. Each possible frequency is a resonant frequency, and the corresponding standing wave pattern is an oscillation mode. For a stretched string of length L with fixed ends, the resonant frequencies are The oscillation mode corresponding to n = 1 is called the fundamental mode or the first harmonic; the mode corresponding to n = 2 is the second harmonic; and so on.
If no friction is present, the mechanical energy E=K+U
remains constant even though K and U change.
The interference of two identical sinusoidal waves moving in opposite directions produces
standing waves.
This is a vector that has a magnitude equal to
the amplitude y_m of the wave and that rotates about an origin with an angular speed equal to the angular frequency ω of the wave.
When two or more waves traverse the same medium,
the displacement of any particle of the medium is the sum of the displacements that the individual waves would give it, an effect known as the principle of superposition for waves.
The frequency f of periodic, or oscillatory, motion is
the number of oscillations per second
If an external driving force with angular frequency ωd acts on an oscillating system with natural angular frequency ω,
the system oscillates with angular frequency ω_d.
The period T is
the time required for one complete oscillation, or cycle
SHM velocity and acceleration as functions of time:
v=-ωx_msin(ωt+Φ) -ωx_m is the velocity amplitude v_m a=-ω^(2)x_mcos(ωt+Φ) -ω^(2)x_m is the acceleration amplitude a_m
The speed of a wave on a string with tension τ and linear density μ is
v=sqrt(T/μ)
The wave speed v (the speed of the wave along the string) is related to these other parameters by
v=ω/k=λ/T=λf
How is angular frequency related to the period and frequency of the motion?
w=2π/T=2πf
If the damping force is given by F_d=-bv,where v is the velocity of the oscillator and b is a damping constant, then the displacement of the oscillator is given by
x(t)=x_me^(-bt/2m)cos(ω't+Φ) where ω', the angular frequency of the damped oscillator, is given by ω'=sqrt((k/m)-(b^(2)/4m^(2)))
In simple harmonic motion (SHM), the displacement of a particle from its equilibrium position is described by the equation
x=x_mcos(ωt+Φ) (displacement) -x_m is the amplitude of displacement -ωt+Φ is the phase of motion -Φ is the phase constant
If the two are traveling in the same direction and have the same amplitude y_m and frequency (hence the same wavelength) but differ in phase by a phase constant Φ, the result is a single wave with this same frequency:
y'(x,t)=[2y_mcos(1/2)Φ)]sin(kx-ωt+(1/2)Φ) -If Φ, the waves are exactly in phase and their interference is fully constructive; if , they are exactly out of phase and their interference is fully destructive.
For a string with fixed ends, the standing wave is given by
y'(x,t)=[2y_msinkx]cosωt
Any function of the form
y(x,t)=h(kx±ωt) -can represent a traveling wave with a wave speed as given above and a wave shape given by the mathematical form of h. The plus sign denotes a wave traveling in the negative direction of the x axis, and the minus sign a wave traveling in the positive direction.
A sinusoidal wave moving in the positive direction of an x axis has the mathematical form
y=(x,t)=y_msin(kx-ωt) -where y_m is the amplitude (magnitude of the maximum displacement) of the wave, k is the angular wave number, ω is the angular frequency, and kx-ω is the phase.
The period T and frequency f of the wave are related to ω by
ω/2π=f=1/T
A particle with mass m that moves under the influence of a Hooke's law restoring force given by is a linear simple harmonic oscillator with
ω=sqrt(k/m) T=2π(sqrt(m/k))
The velocity amplitude v_m of the system is greatest when
ω_d=ω, a condition called resonance. The amplitude xm of the system is (approximately) greatest under the same condition.
A particle in simple harmonic motion has, at any time, kinetic energy
K=(1/2)mv^2
The average power of, or average rate at which energy is transmitted by, a sinusoidal wave on a stretched string is given by
P_avg=(1/2)μvω^2y^2_m
A particle in simple harmonic motion has, at any time, potential energy
U=(1/2)kx^2
Two identical strings each have one end attached to a wall. The other ends are each attached to a separate spool that allows the tension of each string to be changed independently. Consider each of the waves shown. Which one of the following statements is true if the frequency and amplitude of the waves is the same? a) The tension in the string on which wave A is traveling is four times that in the string on which wave D is traveling. b) The tension in the string on which wave B is traveling is four times that in the string on which wave D is traveling. c) The tension in the string on which wave B is traveling is four times that in the string on which wave A is traveling. d) The tension in the string on which wave D is traveling is four times that in the string on which wave A is traveling. e) The tension in the string on which wave C is traveling is four times that in the string on which wave B is traveling.
c) The tension in the string on which wave B is traveling is four times that in the string on which wave A is traveling.
A block is attached to the end of a spring A block is attached to the end of a spring. The block is then displaced from its equilibrium position and released. Subsequently, the block moves in simple harmonic motion without any losses due to friction. Which one of the following statements concerning the total mechanical energy of the block-spring system this situation is true? a) The total mechanical energy is dependent on the amplitude of the motion. b) The total mechanical energy is at its maximum when the block is at its equilibrium position. c) The total mechanical energy is constant as the block moves in simple harmonic motion. d) The total mechanical energy is only dependent on the spring constant and the mass of the block.
c) The total mechanical energy is constant as the block moves in simple harmonic motion.
A tsunami is a fast moving ocean wave train that is produced during an earthquake. Consider such a wave initiated at center of the earthquake off the western coast of South America that reaches the Hawaiian Islands within 15 hours. Which one of the following statements concerning the tsunami is correct? a) The tsunami carried water from the earthquake center to Hawaii, but it did not carry energy to Hawaii from South America. b) The tsunami carried energy and water from the earthquake center to Hawaii. c) The tsunami carried energy from the earthquake center to Hawaii, but it did not carry water to Hawaii from South America. d) The tsunami did not carry energy or water from the earthquake center to Hawaii.
c) The tsunami carried energy from the earthquake center to Hawaii, but it did not carry water to Hawaii from South America.
An object in simple harmonic motion is observed to move between a maximum position and a minimum position. The minimum time that elapses between the object being at its maximum position and when it returns to that maximum position is equal to which of the following parameters? a) frequency b) angular frequency c) period d) amplitude e) wavelength
c) period
What is the term used to describe the situation in which an external driving force is applied to a system with a frequency that equals the natural frequency of the system? a) symbiosis b) synergy c) resonance d) somnoluminescence e) bonnechance
c) resonance
Under which one of the following conditions does the motion of a simple pendulum approximate simple harmonic motion? a) when the pendulum swings rapidly b) when the pendulum swings slowly c) when the pendulum swings through a small angle d) when the pendulum swings through a large angle e) when the length of the pendulum is more than twice the diameter of the bob
c) when the pendulum swings through a small angle
A transverse wave is traveling along a Slinky A transverse wave is traveling along a Slinky. The drawing below represents a section of the Slinky at one instant in time. The direction the wave is traveling is from left to right. Two segments are labeled on the Slinky. At the instant shown, which of the following statements correctly describes the motion of the particles that compose the Slinky in segments A and B? a) In segment A the particles are moving downward and in segment B the particles are moving upward. b) In segment A the particles are moving upward and in segment B the particles are moving upward. c) In segment A the particles are moving downward and in segment B the particles are moving downward. d) In segment A the particles are moving upward and in segment B the particles are moving downward. e) In segment A the particles are moving toward the left and in segment B the particles are moving toward the right.
d) In segment A the particles are moving upward and in segment B the particles are moving downward.
Which one of the following statements concerning the mechanical energy of a harmonic oscillator at a particular point in its motion is true? a) The mechanical energy depends on the acceleration at that point. b) The mechanical energy depends on the velocity at that point. c) The mechanical energy depends on the position of that point. d) The mechanical energy does not vary during the motion. e) The mechanical energy is equal to zero joules if the point is the equilibrium point.
d) The mechanical energy does not vary during the motion.
The tension of a guitar string in increased by a factor of 4 The tension of a guitar string in increased by a factor of 4. How does the speed of a wave on the string increase, if at all? a) The speed of a wave is reduced to one-fourth the value it had before the increase in tension. b) The speed of a wave is reduced to one-half the value it had before the increase in tension. c) The speed of a wave remains the same as before the increase in tension. d) The speed of a wave is increased to two times the value it had before the increase in tension. e) The speed of a wave is increased to four times the value it had before the increase in tension.
d) The speed of a wave is increased to two times the value it had before the increase in tension.
Which one of the following statements explains why a piano and a guitar playing the same musical note sound different? a) The fundamental frequency is different for each instrument. b) The two instruments have the same fundamental frequency, but different harmonic frequencies. c) The two instruments have the same harmonic frequencies, but different fundamental frequencies. d) The two instruments have the same fundamental frequency and the same harmonic frequencies, but the amounts of each of the harmonics is different for the two instruments..
d) The two instruments have the same fundamental frequency and the same harmonic frequencies, but the amounts of each of the harmonics is different for the two instruments..
A sound wave is being emitted from a speaker with a frequency f and an amplitude A. The sound waves travel at a constant speed of 343 m/s in air. Which one of the following actions would reduce the wavelength of the sound waves to one half of their initial value? a) increase the frequency to 2f b) increase the amplitude to 2A c) decrease the frequency to f /4 d) decrease the frequency to f /2 e) decrease the amplitude to A /2
d) decrease the frequency to f /2
Which one of the following units is used for frequency? a) oersted b) second c) farad d) hertz e) gauss
d) hertz
A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of length L. The ball is displaced from its equilibrium position by an angle θ and released. What is the magnitude of the restoring force that moves the ball toward its equilibrium position and produces simple harmonic motion? a) kx b) mg c) mg (cos θ) d) mg (sin θ) e) mgL (sin θ)
d) mg (sin θ)
When a wire is stretched by a force F, the speed of a traveling wave is v. What is the speed of the wave on the wire when the force is doubled to 2F? a) v b) 2v c) 4v d) v(sqrt(2)) e) v/(sqrt(2))
d) v(sqrt(2))
Waves in which the particles of the medium oscillate parallel to the wave's direction of travel are
longitudinal waves.