4AIn the time interval T, the mass goes through one complete oscillation back to the starting point (A+A+A+A)
A mass on a spring in SHM has amplitude A and period T. At what point in the motion is v=0 and a=0 simultaneously?
If both v and a would be zero at the same time, the mass would be at rest and stay at rest. So at no point are both "v" and "a" equal to zero at the same time
A mass oscillates in simple harmonic motion with amplitude A. If the mass is doubled, but the amplitude has not changed, what will happen to the total energy of the system?
The total energy won"t change due to conservation of energy.The total energy is equal to the initial value of the elastic potential energy, which is PE = 0.5ka^2. This doesn"t depend on mass, so a change in mass will not affect the energy of the system
If the amplitude of a simple harmonic oscillator is doubled, which of the following quantities will change the most?
Total mechanical energyFrequency and period do not depend on amplitude at all, so they won"t change. Maximum acceleration and maximum speed do depend on amplitude, and both of these quantities will double. The total energy equals the initial potential energy, which depends on the square of the amplitude, so that will quadruple.
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A glider with a spring attached to each end oscillates with a certain period. If the mass of the glider is doubled, what will happen to the period?
Period will increaseThe period is proportional to the square root of the mass. So an increase in mass will lead to an increase in the period of motion.T = 2pi*squareroot(m/k)
A mass oscillates on a vertical spring with period T. If the whole setup is taken to the Moon, how does the period change?
The period won"t change. The period of SHM only depends on the mass and the spring constant and does not depend on the acceleration due to gravity. By going to the Moon, the value of "g" has been reduced, but that doesn"t affect the period of the oscillating mass-spring system.
Two pendular have the same length, but different masses attached to the string. How do their periods compare?
Period is the same for both cases.The period of a pendulum depends on the length and the acceleration due to gravity, but it does not depend on the mass of the bob.T = 2pi*squareroot(L/g)
Two pendular have different lengths: one with length "L" and the other with length "4L". How do their periods compare?
Period of 4L is two times that of LThe period of a pendulum depends on the length and the acceleration due to gravity. The length dependence goes as the square root of "L", so a pendulum 4 times longer will have a period that is 2 times largerT = 2pi*squareroot(L/g)
After a pendulum starts swinging, its amplitude gradually decreases with time because of friction. What happens to the period of the pendulum during this time?
Period doesn"t changeThe period of a pendulum doesn"t depend on its amplitude, but only on its length and the acceleration due to gravity.T = 2pi*squareroot(L/g)
You"re sitting on a swing. A friend push you, and you start swinging with period "T1". Suppose you were standing on the swing rather than sitting. When given the same push, you start swinging with period "T2". Which of the following is true?
T1 > T2Standing up raises the center of mass of the swing, making it shorter. Since L1 > L2, then T1 > T2T = 2pi*squareroot(L/g)
Yes: all wave types - transverse, longitudinal, surface - have all of these properties: wavelength, frequency, amplitude, velocity, period
At a football game, the "wave" might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as?
Transverse wavePeople are moving up and down, and the wave is traveling around the stadium. Thus, the motion of the wave is perpendicular to the oscillation direction of the people, and so this is a transverse wave.
Microwaves travel with the speed of light (c = 3 x 10^8 m/s). At a frequency of 10 GHz, these waves cause the water molecules in your burrito to vibrate. What"s their wavelength?
Both the velocity and the wavelength of the waveWave speed must change (different medium); frequency doesn"t change (determined by the source). Since "v" has changed and "f" is constant, then lambda (wavelength) must also change
Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?
On a hot dayThe speed of sound in a gas increases with temperature. This is because the molecules are bumping into each other faster and more often, so it"s easier to propagate the compression wave (sound wave)
You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position?
Drops to ¼ its original valueFor a source of a given power "P", the intensity is given by I = P/4pi(r^2). So if distance doubles, the intensity must decrease to one-quarter its original value.
When Mary talks, she creates an intensity level of 60dB at your location. Alice talks with the same volume, also giving 60 dB at your location. If both Mary and Alice talk simultaneously from the same spot, what would be the new intensity level that you hear?
Between 60 dB and 120 dBWith two voices adding up, the intensity increases by only a factor of 2, meaning that the intensity level is higher by an amount equal to: 10log(2) = 3dBThe new intensity level is 63dB.
A quiet radio has an intensity level of about 40 dB. Busy street traffic has a level of about 70 dB. How much greater is the intensity of the street traffic compared to the radio?
About 1000 times.Increase by 10 dB = increase by factor of 10^1 (10)Increase by 20 dB = increase by factor of 10^2 (100)Increase by 30 dB = increase by factor of 10^3 (1000)
You blow into an open pipe and produce a tone. What happens to the frequency of the tone if you close the end of the pip and blow into it again?
You hear a lower frequencyIn the open pipe, 0.5 of a wave "fits" into the pipe, while in the closed pipe, only 0.25 of a wave fits. Because the wavelength is larger in the closed pipe, the frequency will be lower.
When you tune a guitar string, what physical characteristic of the string are you actually changing?
Tension of the stringBy tightening or loosening the knobs on the neck of the guitar, you"re changing the tension of the string. This alters the wave speed and therefore alters the frequency of the fundamental standing wave because f = v/2L
Speakers A and B emit sound waves of 1m, which interfere constructively at a donkey located 200 m away. What happens to the sound intensity if speaker A steps back 2.5 m?
Intensity goes to 0If wavelength is 1m, then a shift of 2.5m corresponds to 2.5lamda, which puts the two waves out of phase, leading to destructive interference. The sound intensity will therefore go to zero.
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You"re heading toward an island in a speedboat and you see your friend standing on these hort, at the base of a cliff. You sound the boat"s horn to alert your friend of your arrive. If the horn has a rest frequency of f0, what frequency does your friend here?
Higher than f0.Due to the approach of the source towards the stationary observer, the frequency is shifted higher. This is the same situation as depicted in the previous question.