The free lower end of the rope is struck sharply at time t=0. What is the time t it takes the resulting wave on the rope to travel to the ceiling, be reflected, and return to the lower end of the rope? Express your answer in terms of L and constants such as g (the magnitude of the acceleration due to gravity), π, etc.

Explanation:

The equation of the velocity of wave is given by:

Here:

So the velocity will be:

We know that the velocity is the variation of the position with respect to time so:

Let's take the integral in both sides:

Solving these two integrals we have:

Therefore the time will be

I hope it helps you!

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.