Chapter 11: Vibrations And Waves
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Questions and Answers
- 1.
The time for one cycle of a periodic process is called the
- A.
Amplitude.
- B.
Wavelength.
- C.
Wavelength.
- D.
Wavelength.
Correct Answer
D. Wavelength.Explanation
The time for one cycle of a periodic process is called the wavelength. This is because wavelength refers to the distance between two corresponding points on a wave, such as the crest or trough. In the context of a periodic process, the wavelength represents the time it takes for the process to complete one full cycle. Therefore, the correct answer is wavelength.Rate this question:
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- 2.
For a periodic process, the number of cycles per unit time is called the
- A.
Amplitude.
- B.
Wavelength.
- C.
Frequency.
- D.
Period.
Correct Answer
C. Frequency.Explanation
The number of cycles per unit time is referred to as the frequency of a periodic process. It represents how many complete cycles occur in a given time interval. The amplitude refers to the maximum displacement from the equilibrium position, the wavelength is the distance between two consecutive points in a wave with the same phase, and the period is the time it takes for one complete cycle to occur. Therefore, the correct answer is frequency.Rate this question:
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- 3.
For vibrational motion, the maximum displacement from the equilibrium point is called the
- A.
Amplitude.
- B.
Wavelength.
- C.
Frequency.
- D.
Period.
Correct Answer
A. Amplitude.Explanation
The maximum displacement from the equilibrium point in vibrational motion is called the amplitude. Amplitude represents the maximum distance that a vibrating object moves from its resting position. It is a measure of the intensity or strength of the vibration. Wavelength refers to the distance between two consecutive points in a wave that are in phase, frequency is the number of oscillations or cycles per second, and period is the time it takes for one complete cycle.Rate this question:
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- 4.
A mass on a spring undergoes SHM. When the mass is at its maximum displacement from equilibrium, its instantaneous velocity
- A.
Is maximum.
- B.
Is less than maximum, but not zero.
- C.
Is zero.
- D.
Cannot be determined from the information given.
Correct Answer
C. Is zero.Explanation
When the mass on a spring is at its maximum displacement from equilibrium, it momentarily stops and changes direction. At this point, the spring is momentarily at rest, resulting in an instantaneous velocity of zero. This occurs because the restoring force of the spring is at its maximum, causing the mass to momentarily come to a stop before accelerating back towards the equilibrium position. Therefore, the correct answer is that the instantaneous velocity is zero.Rate this question:
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- 5.
A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, its instantaneous velocity
- A.
Is maximum.
- B.
Is less than maximum, but not zero.
- C.
Is zero.
- D.
Cannot be determined from the information given.
Correct Answer
A. Is maximum.Explanation
When a mass on a spring undergoes simple harmonic motion (SHM), its velocity is constantly changing. As the mass passes through the equilibrium position, it momentarily stops and changes direction. At this point, the velocity is at its maximum because it is changing from positive to negative or vice versa. Therefore, the correct answer is that the instantaneous velocity is maximum when the mass passes through the equilibrium position.Rate this question:
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- 6.
A mass on a spring undergoes SHM. When the mass is at maximum displacement from equilibrium, its instantaneous acceleration
- A.
Is a maximum.
- B.
Is less than maximum, but not zero.
- C.
Is zero.
- D.
Cannot be determined from the information given
Correct Answer
A. Is a maximum.Explanation
When a mass on a spring undergoes simple harmonic motion (SHM), its acceleration is directly proportional to its displacement from equilibrium. Therefore, when the mass is at maximum displacement from equilibrium, its acceleration is also at a maximum. This is because the force acting on the mass is at its maximum at this point, leading to a maximum acceleration.Rate this question:
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- 7.
A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a minimum?
- A.
At either A or B
- B.
Midway between A and B
- C.
One-fourth of the way between A and B
- D.
One-fourth of the way between A and B
Correct Answer
A. At either A or BExplanation
When the mass is at either point A or point B, it is at the extreme positions of its motion. At these points, the mass momentarily stops and changes direction. Therefore, its velocity is zero, and since kinetic energy is directly proportional to the square of velocity, the kinetic energy is also zero. This means that the kinetic energy is at its minimum when the mass is located at either point A or point B.Rate this question:
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- 8.
A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?
- A.
At either A or B
- B.
Midway between A and B
- C.
One-fourth of the way between A and B
- D.
None of the above
Correct Answer
B. Midway between A and BExplanation
When the mass is located midway between points A and B, its kinetic energy is at a maximum. This is because at this point, the mass has reached its maximum velocity and is moving with the highest speed. As the mass moves away from this point, its velocity decreases, resulting in a decrease in kinetic energy. Therefore, the mass is not located at either A or B when its kinetic energy is a maximum. Similarly, the mass being located one-fourth of the way between A and B does not correspond to the maximum kinetic energy.Rate this question:
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- 9.
A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a minimum?
- A.
At either A or B
- B.
Midway between A and B
- C.
One-fourth of the way between A and B
- D.
None of the above
Correct Answer
B. Midway between A and BExplanation
When the mass is at the midpoint between points A and B, its potential energy is at a minimum. This is because at this position, the spring is neither stretched nor compressed, resulting in the lowest potential energy. As the mass moves away from the midpoint towards either A or B, the spring is either stretched or compressed, increasing the potential energy. Therefore, the mass is located midway between A and B when its potential energy is a minimum.Rate this question:
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- 10.
A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a maximum?
- A.
At either A or B
- B.
Midway between A and B
- C.
One-fourth of the way between A and B
- D.
None of the above
Correct Answer
A. At either A or BExplanation
The potential energy of a mass attached to a vertical spring is maximum when the mass is at either point A or point B. This is because at these points, the spring is stretched or compressed to its maximum extent, resulting in the highest potential energy. At any other point between A and B, the spring is neither fully stretched nor fully compressed, resulting in lower potential energy. Therefore, the mass is located at either A or B when its potential energy is a maximum.Rate this question:
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- 11.
Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
- A.
Increases the energy by a factor of two
- B.
Ncreases the energy by a factor of three
- C.
Increases the energy by a factor of four
- D.
Produces no change
Correct Answer
C. Increases the energy by a factor of fourExplanation
Doubling the amplitude of a vibrating mass-and-spring system increases the mechanical energy by a factor of four. This is because the mechanical energy of a vibrating system is directly proportional to the square of the amplitude. Therefore, when the amplitude is doubled, the mechanical energy increases by a factor of four (2^2 = 4).Rate this question:
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- 12.
Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
- A.
Increases the energy by a factor of two
- B.
Increases the energy by a factor of three
- C.
Increases the energy by a factor of four
- D.
Produces no change
Correct Answer
D. Produces no changeExplanation
Doubling the mass of a vibrating mass-and-spring system does not produce any change in the system's mechanical energy. The mechanical energy of a mass-and-spring system is determined by the amplitude of the vibration and the spring constant, but not the mass. Therefore, increasing the mass does not affect the mechanical energy of the system.Rate this question:
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- 13.
Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
- A.
Increases the energy by a factor of two
- B.
Increases the energy by a factor of three
- C.
Increases he energy by a factor of four
- D.
Produces no change
Correct Answer
A. Increases the energy by a factor of twoExplanation
Doubling the spring constant of a vibrating mass-and-spring system increases the system's mechanical energy by a factor of two. This is because the spring constant is directly proportional to the potential energy stored in the spring. Increasing the spring constant results in a stiffer spring, which allows for more energy to be stored in the system. As a result, the mechanical energy of the system is doubled.Rate this question:
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- 14.
A mass oscillates on the end of a spring, both on Earth and on the Moon. Where is the period the greatest?
- A.
Earth
- B.
The Moon
- C.
Same on both Earth and the Moon
- D.
Cannot be determined from the information given
Correct Answer
C. Same on both Earth and the MoonExplanation
The period of oscillation is determined by the mass and the spring constant, both of which remain constant regardless of the location. Therefore, the period will be the same on both Earth and the Moon.Rate this question:
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- 15.
Increasing the spring constant k of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's mass m.)
- A.
The frequency increases.
- B.
The frequency decreases.
- C.
There is no change in the frequency.
- D.
The frequency increases if the ratio k/m is greater than or equal to 1 and decreases if the ratio k/m is less than 1.
Correct Answer
A. The frequency increases.Explanation
When the spring constant k of a mass-and-spring system is increased, the resonant frequency of the system also increases. This is because the resonant frequency is inversely proportional to the square root of the spring constant. Therefore, as the spring constant increases, the resonant frequency increases as well.Rate this question:
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- 16.
Increasing the mass M of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's spring constant k.)
- A.
The frequency increases.
- B.
The frequency decreases.
- C.
There is no change in the frequency.
- D.
The frequency increases if the ratio k/m is greater than or equal to 1 and decreases if the ratio k/m is less than 1.
Correct Answer
B. The frequency decreases.Explanation
When the mass of a mass-and-spring system is increased, the resonant frequency of the system decreases. This can be explained by the equation for the resonant frequency of a mass-spring system, which is given by f = (1/2π)√(k/m), where f is the frequency, k is the spring constant, and m is the mass. As the mass is increased, the denominator of the equation increases, causing the overall frequency to decrease. Therefore, increasing the mass of the system results in a decrease in the resonant frequency.Rate this question:
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- 17.
Increasing the amplitude of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no other changes in the system.)
- A.
The frequency increases.
- B.
The frequency decreases.
- C.
There is no change in the frequency.
- D.
The frequency depends on the displacement, not the amplitude.
Correct Answer
C. There is no change in the frequency.Explanation
The resonant frequency of a mass-and-spring system is determined by the mass and stiffness of the system, not the amplitude. Therefore, increasing the amplitude of the system will not cause any change in the resonant frequency.Rate this question:
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- 18.
A mass m hanging on a spring has a natural frequency f. If the mass is increased to 4m, what is the new natural frequency?
- A.
4f
- B.
2f
- C.
0.5f
- D.
0.25f
Correct Answer
C. 0.5fExplanation
When the mass hanging on the spring is increased to 4m, the new natural frequency will be 0.5f. This is because the natural frequency of a mass-spring system is inversely proportional to the square root of the mass. When the mass is increased by a factor of 4, the square root of the mass is doubled, resulting in a halving of the natural frequency. Therefore, the new natural frequency is 0.5f.Rate this question:
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- 19.
A simple pendulum consists of a mass M attached to a weightless string of length L. For this system, when undergoing small oscillations
- A.
The frequency is proportional to the amplitude.
- B.
The period is proportional to the amplitude.
- C.
The frequency is independent of the mass M.
- D.
The frequency is independent of the length L.
Correct Answer
C. The frequency is independent of the mass M.Explanation
The frequency of a simple pendulum is determined by the length of the string and the acceleration due to gravity, but it is independent of the mass. This is because the mass does not affect the time it takes for the pendulum to swing back and forth. The only factors that affect the frequency are the length of the string and the strength of gravity. Therefore, the frequency of a simple pendulum is independent of the mass M.Rate this question:
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- 20.
When the mass of a simple pendulum is tripled, the time required for one complete vibration
- A.
Increases by a factor of 3.
- B.
Does not change.
- C.
Decreases to one-third of its original value.
- D.
Decreases to 1/√3 of its original value.
Correct Answer
B. Does not change.Explanation
When the mass of a simple pendulum is tripled, the time required for one complete vibration does not change. This is because the period of a simple pendulum, which is the time required for one complete vibration, depends only on the length of the pendulum and the acceleration due to gravity. The mass of the pendulum does not affect the period. Therefore, tripling the mass of the pendulum will not change the time required for one complete vibration.Rate this question:
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- 21.
Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period of B?
- A.
0.71T
- B.
T
- C.
1.4T
- D.
2T
Correct Answer
B. TExplanation
The period of a pendulum is determined by the length of the pendulum and the acceleration due to gravity. Since both pendulum A and B have the same length of 3.0 m, their periods should be the same if the only difference is the weight. Since pendulum A is twice as heavy as pendulum B, it means that pendulum A will take twice as long to complete one full swing compared to pendulum B. Therefore, the period of pendulum B is T.Rate this question:
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- 22.
When the length of a simple pendulum is tripled, the time for one complete vibration increases by a factor of
- A.
3.
- B.
2.
- C.
1.7.
- D.
1.4.
Correct Answer
C. 1.7.Explanation
When the length of a simple pendulum is tripled, the time for one complete vibration increases. This is because the time period of a simple pendulum is directly proportional to the square root of its length. When the length is tripled, the square root of the length is also increased by a factor of √3. Therefore, the time for one complete vibration increases by a factor of approximately 1.7.Rate this question:
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- 23.
What happens to a simple pendulum's frequency if both its length and mass are increased?
- A.
It increases.
- B.
It decreases.
- C.
It remains constant.
- D.
It could remain constant, increase, or decrease; it depends on the length to mass ratio.
Correct Answer
B. It decreases.Explanation
When both the length and mass of a simple pendulum are increased, the frequency of the pendulum decreases. This is because the frequency of a pendulum is inversely proportional to the square root of the length, and directly proportional to the square root of the mass. So, as both the length and mass increase, the square root of the length increases, while the square root of the mass also increases. As a result, the frequency decreases.Rate this question:
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- 24.
Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?
- A.
Pendulum B is twice as long as A.
- B.
Pendulum B is twice as massive as A.
- C.
The length of B is four times the length of A.
- D.
The mass of B is four times the mass of A.
Correct Answer
C. The length of B is four times the length of A.Explanation
The frequency of a simple pendulum is inversely proportional to its length. If pendulum A swings back and forth at twice the frequency of pendulum B, it means that pendulum A has a shorter length than pendulum B. Since the frequency is inversely proportional to the length, if the frequency is doubled, the length must be halved. Therefore, the length of B is four times the length of A.Rate this question:
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- 25.
If you take a given pendulum to the Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum will
- A.
Increase.
- B.
Decrease.
- C.
Not change.
- D.
Either increase or decrease; it depends on its length to mass ratio.
Correct Answer
B. Decrease.Explanation
When a pendulum is taken to the Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum will decrease. This is because the resonant frequency of a pendulum is directly proportional to the square root of the acceleration due to gravity. As the acceleration of gravity decreases on the Moon, the resonant frequency of the pendulum will also decrease.Rate this question:
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- 26.
For a forced vibration, the amplitude of vibration is found to depend on the
- A.
Sum of the external frequency and the natural frequency.
- B.
Difference of the external frequency and the natural frequency.
- C.
Product of the external frequency and the natural frequency.
- D.
Ratio of the external frequency and the natural frequency.
Correct Answer
B. Difference of the external frequency and the natural frequency.Explanation
In forced vibration, the external frequency and the natural frequency of the system are different. The amplitude of vibration is determined by the difference between these two frequencies. If the external frequency is close to the natural frequency, the amplitude will be high. However, if the external frequency is significantly different from the natural frequency, the amplitude will be low. Therefore, the correct answer is the difference of the external frequency and the natural frequency.Rate this question:
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- 27.
In a wave, the maximum displacement of points of the wave from equilibrium is called the wave's
- A.
Speed.
- B.
Frequency.
- C.
Wavelength.
- D.
Amplitude.
Correct Answer
D. Amplitude.Explanation
The maximum displacement of points of a wave from equilibrium is called its amplitude. Amplitude represents the strength or intensity of the wave. It is measured from the equilibrium position to the highest point of the wave or the lowest point of the wave. It is not related to the speed, frequency, or wavelength of the wave.Rate this question:
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- 28.
The distance between successive crests on a wave is called the wave's
- A.
Speed.
- B.
Frequency.
- C.
Wavelength.
- D.
Amplitude.
Correct Answer
C. Wavelength.Explanation
The distance between successive crests on a wave is called the wavelength. Wavelength is a physical quantity that measures the distance between two identical points on a wave, such as two crests or two troughs. It is usually represented by the symbol λ (lambda). The wavelength of a wave is inversely proportional to its frequency, meaning that shorter wavelengths correspond to higher frequencies and vice versa.Rate this question:
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- 29.
The number of crests of a wave passing a point per unit time is called the wave's
- A.
Speed.
- B.
Frequency.
- C.
Wavelength.
- D.
Amplitude.
Correct Answer
B. Frequency.Explanation
The number of crests of a wave passing a point per unit time is called the wave's frequency. Frequency refers to how often a wave passes a given point in a specific time period. It is measured in hertz (Hz), which represents the number of cycles per second. The speed of a wave, on the other hand, refers to how fast the wave is traveling through a medium. Wavelength is the distance between two consecutive crests or troughs of a wave. Amplitude, on the other hand, refers to the maximum displacement of a wave from its equilibrium position.Rate this question:
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- 30.
For a wave, the frequency times the wavelength is the wave's
- A.
Speed.
- B.
Amplitude.
- C.
Intensity.
- D.
Power.
Correct Answer
A. Speed.Explanation
The relationship between frequency and wavelength is given by the equation speed = frequency × wavelength. This equation states that the speed of a wave is equal to the product of its frequency and wavelength. Therefore, the correct answer is speed.Rate this question:
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- 31.
The frequency of a wave increases. What happens to the distance between successive crests if the speed remains constant?
- A.
It increases.
- B.
It remains the same.
- C.
It decreases.
- D.
It cannot be determined from the information given.
Correct Answer
C. It decreases.Explanation
As the frequency of a wave increases, the distance between successive crests decreases. This is because frequency is directly proportional to the number of crests passing a fixed point per unit time. Therefore, if the frequency increases while the speed remains constant, the crests will be closer together, resulting in a decrease in the distance between them.Rate this question:
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- 32.
Consider a traveling wave on a string of length L, mass M, and tension T. A standing wave is set up. Which of the following is true?
- A.
The wave velocity depends on M, L, T.
- B.
The wavelength of the wave is proportional to the frequency.
- C.
The particle velocity is equal to the wave velocity.
- D.
The wavelength is proportional to T.
Correct Answer
A. The wave velocity depends on M, L, T.Explanation
The wave velocity on a string depends on the mass (M), length (L), and tension (T) of the string. This can be explained by the wave equation v = √(T/μ), where v is the wave velocity and μ is the linear mass density of the string (μ = M/L). As the tension or mass of the string increases, the wave velocity also increases. Similarly, if the length of the string is increased, the wave velocity decreases. Therefore, the statement "The wave velocity depends on M, L, T" is true.Rate this question:
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- 33.
A string of mass m and length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m, with no change in length?
- A.
0.5v
- B.
0.71v
- C.
1.4v
- D.
2v
Correct Answer
B. 0.71vExplanation
When the mass of the string is increased to 2m, with no change in length, the speed of the wave in the string will decrease. This is because the speed of a wave in a string is inversely proportional to the square root of the mass per unit length. Therefore, when the mass is doubled, the speed of the wave will decrease by a factor of square root of 2, which is approximately 0.71. Hence, the speed of the wave in the string will be 0.71v.Rate this question:
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- 34.
A string of mass m and length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L, with no change in mass?
- A.
0.5v
- B.
0.71v
- C.
1.4v
- D.
2v
Correct Answer
C. 1.4vExplanation
When the length of the string is doubled to 2L, the speed of the wave in the string will also double. This is because the speed of a wave in a string is directly proportional to the square root of the tension in the string and inversely proportional to the square root of the linear density (mass per unit length) of the string. Since the mass of the string remains unchanged, the linear density remains the same. Therefore, the speed of the wave will be 2v, which is 1.4 times the original speed v.Rate this question:
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- 35.
A string of mass m and length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T?
- A.
0.5T
- B.
0.71T
- C.
1.4T
- D.
2T
Correct Answer
C. 1.4TExplanation
When the tension in the string is increased to 2T, the speed of the wave in the string will also increase. The relationship between tension and wave speed in a string is given by the equation v = √(T/μ), where v is the wave speed, T is the tension, and μ is the linear mass density of the string. Since the mass and length of the string are constant, the linear mass density remains the same. Therefore, when the tension is increased to 2T, the wave speed will be √(2T/μ), which is equal to 1.4T.Rate this question:
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- 36.
In seismology, the S wave is a transverse wave. As an S wave travels through the Earth, the relative motion between the S wave and the particles is
- A.
Parallel.
- B.
Perpendicular.
- C.
First parallel, then perpendicular.
- D.
First perpendicular, then parallel.
Correct Answer
B. Perpendicular.Explanation
The S wave in seismology is a transverse wave, meaning that the particles vibrate perpendicular to the direction of wave propagation. This means that as the S wave travels through the Earth, the relative motion between the S wave and the particles is perpendicular.Rate this question:
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- 37.
In seismology, the P wave is a longitudinal wave. As a P wave travels through the Earth, the relative motion between the P wave and the particles is
- A.
Parallel.
- B.
Perpendicular.
- C.
First parallel, then perpendicular.
- D.
First perpendicular, then parallel.
Correct Answer
A. Parallel.Explanation
The P wave, also known as the primary wave, is a type of seismic wave that travels through the Earth. It is a longitudinal wave, meaning that the particles in the medium vibrate in the same direction as the wave is moving. Therefore, the relative motion between the P wave and the particles is parallel.Rate this question:
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- 38.
The intensity of a wave is
- A.
Proportional to both the amplitude squared and the frequency squared
- B.
Proportional to the amplitude squared and inversely proportional to the frequency squared.
- C.
Inversely proportional to the amplitude squared and proportional to the frequency squared.
- D.
Inversely proportional to both the amplitude squared and the frequency squared.
Correct Answer
A. Proportional to both the amplitude squared and the frequency squaredExplanation
The intensity of a wave is proportional to both the amplitude squared and the frequency squared because the amplitude of a wave determines its energy, and squaring the amplitude gives us a measure of the energy carried by the wave. Similarly, the frequency of a wave determines the number of oscillations per unit time, and squaring the frequency gives us a measure of the power or rate at which the wave carries energy. Therefore, the intensity of a wave is determined by both the amplitude squared and the frequency squared.Rate this question:
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- 39.
A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?
- A.
Both are right side up.
- B.
The reflected pulse returns right side up while the transmitted pulse is inverted.
- C.
The reflected pulse returns inverted while the transmitted pulse is right side up.
- D.
Both are inverted.
Correct Answer
C. The reflected pulse returns inverted while the transmitted pulse is right side up.Explanation
When a wave pulse travels from a lighter medium to a heavier medium, it experiences a change in direction due to the change in speed. In this case, as the rope becomes thicker and heavier, the reflected pulse returns inverted, meaning it is upside down compared to the original pulse. On the other hand, the transmitted pulse is right side up, meaning it maintains its original orientation as it continues propagating through the thicker and heavier rope.Rate this question:
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- 40.
Two wave pulses with equal positive amplitudes pass each other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy the same region of space at the same time
- A.
Constructive interference occurs.
- B.
Destructive interference occurs.
- C.
A standing wave is produced.
- D.
A traveling wave is produced.
Correct Answer
A. Constructive interference occurs.Explanation
When two wave pulses with equal positive amplitudes pass each other on a string, they undergo constructive interference. This means that the amplitudes of the two pulses add up to create a larger amplitude at the point where they overlap. This occurs because the peaks of one pulse align with the peaks of the other pulse, resulting in a combined wave with a higher amplitude.Rate this question:
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- 41.
Two wave pulses pass each other on a string. The one traveling toward the right has a positive amplitude, while the one traveling toward the left has an equal amplitude in the negative direction. At the point that they occupy the same region of space at the same time
- A.
Constructive interference occurs.
- B.
Destructive interference occurs.
- C.
A standing wave is produced.
- D.
A traveling wave is produced.
Correct Answer
B. Destructive interference occurs.Explanation
When two wave pulses pass each other on a string, they superpose or combine at the point where they occupy the same region of space at the same time. In this case, the wave traveling toward the right has a positive amplitude, while the wave traveling toward the left has an equal amplitude in the negative direction. When these two waves combine, their amplitudes add up, resulting in destructive interference. Destructive interference occurs when two waves with equal amplitudes but opposite phases cancel each other out, resulting in a decrease or complete elimination of the resultant wave. Therefore, destructive interference occurs in this scenario.Rate this question:
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- 42.
Resonance in a system, such as a string fixed at both ends, occurs when
- A.
It is oscillating in simple harmonic motion.
- B.
Its frequency is the same as the frequency of an external source.
- C.
Its frequency is greater than the frequency of an external source.
- D.
Its frequency is smaller than the frequency of an external source.
Correct Answer
B. Its frequency is the same as the frequency of an external source.Explanation
When resonance occurs in a system, such as a string fixed at both ends, it means that the system is vibrating at its natural frequency. This natural frequency is the same as the frequency of an external source that is causing the oscillation. In other words, the system is in sync with the external source, resulting in a stronger and more pronounced vibration. When the frequencies match, constructive interference occurs, amplifying the vibrations and creating resonance in the system.Rate this question:
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- 43.
If one doubles the tension in a violin string, the fundamental frequency of that string will increase by a factor of
- A.
2.
- B.
4.
- C.
1.4.
- D.
1.7.
Correct Answer
C. 1.4.Explanation
When the tension in a violin string is doubled, the fundamental frequency of the string will increase by a factor of 1.4. This can be explained by the relationship between tension and frequency in a string. According to the equation for the fundamental frequency of a vibrating string, the frequency is directly proportional to the square root of the tension. When the tension is doubled, the square root of the tension is multiplied by √2, which is approximately 1.4. Therefore, the fundamental frequency of the string will increase by a factor of 1.4.Rate this question:
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- 44.
What is the spring constant of a spring that stretches 2.00 cm when a mass of 0.600 kg is suspended from it?
- A.
0.300 N/m
- B.
30.0 N/m
- C.
2.94 N/m
- D.
294 N/m
Correct Answer
D. 294 N/mExplanation
The spring constant is a measure of the stiffness of a spring and is defined as the force required to stretch or compress the spring by a certain amount. In this question, a mass of 0.600 kg is suspended from the spring, causing it to stretch by 2.00 cm. Using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement, we can calculate the spring constant. The formula for the spring constant is k = F/x, where F is the force and x is the displacement. Given that the force is equal to the weight of the mass (F = mg), and the displacement is 2.00 cm (or 0.02 m), we can substitute the values into the formula to find k = (0.600 kg)(9.8 m/s^2) / 0.02 m = 294 N/m. Therefore, the correct answer is 294 N/m.Rate this question:
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- 45.
A mass is attached to a spring of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the amplitude?
- A.
0.030 m
- B.
0.083 m
- C.
0.30 m
- D.
0.83 m
Correct Answer
B. 0.083 mExplanation
The amplitude of an oscillating mass-spring system can be determined using the equation:
Amplitude = (Force / (Spring constant)) * (1 / (2π * Frequency))
In this case, the force is 5.0 N and the spring constant is 60 N/m. The frequency can be calculated using the formula:
Frequency = 1 / Period
The period is given as 0.50 s. Therefore, the frequency is 1 / 0.50 = 2 Hz.
Substituting the values into the amplitude equation:
Amplitude = (5.0 N / 60 N/m) * (1 / (2π * 2 Hz))
Amplitude = 0.083 m
Therefore, the amplitude is 0.083 m.Rate this question:
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- 46.
A mass is attached to a spring of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the period of oscillation?
- A.
0.50 s
- B.
1.0 s
- C.
1.5 s
- D.
2.0 s
Correct Answer
D. 2.0 sExplanation
The period of oscillation is the time it takes for one complete cycle of oscillation. In this case, the mass is attached to a spring and is oscillating back and forth. The time it takes for the mass to go back to its equilibrium position is 0.50 s. Since one complete cycle consists of the mass going from one extreme position to the other and back to the equilibrium position, the period of oscillation is twice the time it takes for the mass to go back to its equilibrium position. Therefore, the period of oscillation is 2.0 s.Rate this question:
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- 47.
A mass is attached to a spring of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the frequency of oscillation?
- A.
0.50 Hz
- B.
1.0 Hz
- C.
1.5 Hz
- D.
2.0 Hz
Correct Answer
A. 0.50 HzExplanation
The frequency of oscillation can be calculated using the formula: frequency = 1 / time period. The time period is the time taken for one complete oscillation. In this case, the mass takes 0.50 s to go back to its equilibrium position, so the time period is 0.50 s. Therefore, the frequency of oscillation is 1 / 0.50 = 2.0 Hz.Rate this question:
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- 48.
A mass on a spring undergoes SHM. It goes through 10 complete oscillations in 5.0 s. What is the period?
- A.
0.020 s
- B.
0.50 s
- C.
2.0 s
- D.
50 s
Correct Answer
B. 0.50 sExplanation
The period of an oscillation is the time it takes for one complete cycle or one complete oscillation. In this case, the mass on a spring goes through 10 complete oscillations in 5.0 s. Therefore, to find the period, we divide the total time by the number of oscillations. 5.0 s divided by 10 oscillations gives us 0.50 s, which is the correct answer.Rate this question:
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- 49.
A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion with amplitude 4.0 cm. What is the energy of the system now?
- A.
2.0 J
- B.
4.0 J
- C.
8.0 J
- D.
16 J
Correct Answer
C. 8.0 JExplanation
When the mass is cut in half, the amplitude of the motion remains the same. However, the energy of the system is directly proportional to the mass. Since the mass is halved, the energy of the system is also halved. Therefore, the energy of the system now is 8.0 J.Rate this question:
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- 50.
A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?
- A.
0.024 m
- B.
0.058 m
- C.
0.24 m
- D.
0.58 m
Correct Answer
C. 0.24 mExplanation
The amplitude of vibration can be determined using the equation for the speed of an object in simple harmonic motion at the equilibrium position, which is given by v = ωA, where v is the speed, ω is the angular frequency, and A is the amplitude. Rearranging the equation, we have A = v/ω. Since the speed is given as 1.5 m/s and the angular frequency can be calculated using the formula ω = √(k/m), where k is the spring constant and m is the mass, we can substitute the given values to find A = 1.5/√(20/0.50) = 0.24 m.Rate this question:
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Mar 20, 2023Quiz Edited by
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Sep 25, 2012Quiz Created by
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