honors physics - waves

A mass on a spring in SHM has an amplitude (A) and period (T).

What is the total distance traveled by the mass after a time interval (t)?

4A. The amplitude (A) is the distance from equilibrium to max displacement. During one complete cycle (a period of motion), this distance is traveled 4 times

A mass on a spring in SHM has an amplitude (A) and period (T).

What is the net displacement of the mass after a time interval (t)?

0\. Since the object starts its motion over after completing one period (by definition), then its total displacement must be zero over an entire period

A mass on a spring in SHM has an amplitude (A) and period (T).

How long does it take for the mass to travel a total distance of 6A?

1\.5 T. In 1 period it travels 4 amplitudes, in the other 0.5 period, it would travel 2 amplitudes

A mass on a spring in SHM has an amplitude (A) and period (T).

What points in the motion is v=0 and a=0 simultaneously?

None. Both quantities are always changing (sinusoidally) and will equal zero at various times, but never at the same time. When v=0, the acceleration is maximum, and when a=0, velocity is maximum

A hole is drilled through the center of the Earth and emerges on the other side. You jump into the hole.

What happens to you?

You fall to the other side of Earth and then return. This is much like a mass on a spring. Earth’s gravitational field reaches 0 N/kg at the center (since you’d be pulled in all directions equally by the surrounding Earth). If you were to jump into the hole, you’d oscillate back and forth

A mass oscillates in SHM with amplitude (A).

If the mass is doubled, but the amplitude is not changed, what will happen to the total energy of the system?

The total energy will not change. Energy of the oscillator does not depend on the mass, just the amplitude and the spring constant

If the amplitude of a simple harmonic is doubled, what will change the most?

Total mechanic energy. Energy is proportional to the square of the amplitude. All the other quantities are either independent of the amplitude (frequency and period) or proportional to the amplitude (the 1st power, not the 2nd power)

A glider with a spring attached to each end oscillates with a certain period.

If the mass of the glider doubled, what will happen to the period?

Period will increase. Period increases as it will take longer for the spring to oscillate the greater mass (it resists acceleration more, and so it won’t accelerate as much, nor travel as fast as before

A mass is suspended from the ceiling of an elevator by a spring. When the elevator is at rest, the period is T.

What happens to period when the elevator is moving upward at a constant speed?

Period will not change. There is nothing special about being at rest. In terms of physics involved, there is no difference between being at rest, or moving at a constant speed

A mass is suspended from the ceiling of an elevator by a spring. When the elevator is at rest, the period is T.

What happens to period when the elevator is accelerating upward?

Period will not change. The period of oscillation does not depend at all on whether or not the oscillator itself is accelerating. One could think of the accelerating elevator as an artificial gravity field… which doesn’t impact the period of a mass oscillating on a spring

A mass oscillates on a vertical spring with period (T).

If the whole setup is taken to the moon, how does the period change?

Period will not change as the period does not depend on the local acceleration due to gravity

Two pendula have the same length, but different masses attached to the string.

How do their period compare?

Period is the same for both cases. Period of a pendulum does not depend at all on the mass of the bob

A grandfather clock has a weight at the bottom of the pendulum that can be moved up or down.

If the clock is running slow, what should you do to adjust the time properly?

Move the weight up. Moving it up effectively shortens the length of a physical pendulum, which makes the period shorter

A pendulum is suspended from the ceiling of an elevator. When the elevator is at rest, the period is T.

What happens to period when the elevator is accelerating upward?

Period will decrease. The elevator here is acting like an artificial gravity field (just as you would feel heavier, the pendulum does also). Even though the weight of the bob doesn’t affect the period, the value of g does. If g is higher, then the period would be shorter (it would oscillate more quickly back and forth and take less time to do so)

A swinging pendulum has period (T) on Earth.

If the same pendulum were moved to the moon, how does the new period compare to the old period?

Period increases. Period is inversely related the square root of g. If g decreases, T increases

Consider a wave on a string moving to the right.

What is the direction of the velocity of a particle at a crest?

Down. At the crest of the wave, the particle is momentarily at rest as its direction of motion is changing from up to down (or vice versa)

Consider a wave on a string moving to the right.

What is the direction of the velocity of a particle at a node?

Up. Since the wave is moving left to right, you might notice that to the left of the dot, the wave form is above the equilibrium position. A movement or two later, the dot would then be at that location (above the equilibrium) so it is moving upward at that time

A boat is moored in a fixed location, and waves make it move up and down. If the spacing between the wave crests is 20 m and the speed of the wave is 5 m/s,

how long does it take the boat to go from the top of a crest to the bottom of a trough?

2 seconds. Calculate the period using the velocity of a wave equation. V = wavelength/ period, so Period = wavelength/ velocity or 20/ 5 = 4 seconds. From a crest to trough is 1/2 a period, so time is 2 seconds

A wave pulse can be sent down a rope by jerking sharply on the free end.

If the tension of the rope is increased, how will that affect the speed of the wave?

Speed increases. Increasing the tension the restoring force between particles (sort of like increasing the spring constant for a mass on a spring). This makes the oscillation of the disturbance occur more quickly, which means that the disturbance can pass through the medium more quickly (a greater wave speed)