Unraveling the Mysteries of Earthquakes, Longitudinal & Transverse Waves

[thunderfvck]

Hello!

Okay, here we go.

Q1. A block is resting on top of a flat plate that is oscillating vertically with simple harmonic motion. If the frequency of the plate's oscillation is 2.0 Hz, what is the maximum amplitude it can have before the block loses contact with the plate?

- This question boggles my mind! Okay, So I figure that the block will lose contact with the plate once the plate reaches its maximum height (it's amplitude). Then the plate will begin to accelerate downwards while the block is left to go downwards with gravity's acceleration, which will be much less I imagine. And this is where the block will be hanging in the air while the plate goes down. But how do I know when this happens? All I have is the frequency, I don't see how I can get the amplitude.
- I also was thinking about energy. At the highest point the velocity of the block/the plate will be zero. Zero kinetic energy, maximum potential energy. But I don't have anything to work with but the frequency!

- With the frequency I can find the angular frequency (w).
- w = (2pi)*f
- The equation for the displacement of an object in SHM is x(t) = Acos(wt + d). A is the amplitude, d is the phase constant)
- The maximum velocity is given by v = -wA.
- The maxium acceleration is given by a = (-w^2)A

The answer is 6.2 (I'm not sure about the units, I didn't bother to write them down).

Q2. A physics student holds one end of a stretched spring and generates a pulse by flicking his hand quickly up and down. If he does this flicking action more slowly, how will the length of the pulse and the speed of the pulse along the spring be affected?

- I was never too sure about this kind of problem, even though we did a lab on it. Okay, so if he does it more slowly, that means he's reducing the period, right? Okay, let me try to work this out with the equations. I don't know if this is how it is done, so please tell me where I'm going wrong.
- v = sqrt(F/u), where v is the wave speed, F is the tension in the spring, and u is the linear mass density of the spring. So, the velocity of the wave does NOT depend on anything I'm doing to the spring, whether I'm doing it faster or slower. It is totally dependent on F and u which is unique to the spring itself.
- v = f(wl) where v is the wave speed, f is the frequency and wl is the wavelength. So, if my velocity is kept constant, then by flicking the spring more slowly I can only alter the frequency or the wavelength. By flicking it slower, the period by which my hand is moving back and forth is reduced, and so the frequency is increased. And consequently, the wavelength must be reduced such that v = f(wl). Is this correct?

Q3. An earthquake generates both longitudinal waves and transverse waves which move through the Earth at about 5 km/s and 3 km/s respectively. At a detection center the arrival times of the two types of waves can be registered. How many separate detection centers are necessary to pinpoint the epicenter of an earthquake?

- This one seems hard. Would you only need two? Because if you had one, then you wouldn't really have much to work with aside from the fact that it took x time to reach the center. If you had two, at least you can say which one is closer and you'd have an idea where it might have originated. But three would always be better, and two hundred would be even better...So, which is it?

And that's about it for now! Other than this I think I have everything covered. THank you so much for any replies!

 

[Tide]

Q1: The block will lose contact if the acceleration of the plate exceeds the gravitational acceleration.

 

[thunderfvck]

Ah, of course!

That works out perfectly to give 6.2 cm. Thank you!

Do I have the right idea for Q2? That is probably the most important question that needs answering. I believe I am correct, because it coorelates with the answers to a quiz I had failed earlier.