Observe that the given vector field is a gradient field:
Let 
, so that
Integrating the first equation with respect to 
, we get
Differentiating this with respect to 
gives
Now differentiating 
with respect to 
gives
Putting everything together, we find a scalar potential function whose gradient is 
,
It follows that the curl of is 0 (i.e. the zero vector).
Answer:
Primary waves (P-waves)
Explanation:
Due to excess of the energy inside the earth when the tectonic plates begin to slide or fracture then the energy is released in the form of seismic waves, this causes the earthquake.
<u>Two types of seismic waves are generally responsible for the earth quakes:</u>
- body waves
- surface waves
Body waves are of two types:
Primary waves (P-waves)
These are the fastest of all the waves involved in the earth-quake which travel at a speed of 1.6 km to 8 km per second.
They can pass trough solids, liquids and gases. They arrive at the surface as an instant thud.
Secondary waves (S-waves)
They can only pass through the solids and they move slower than the P-waves.
As S-waves move, they displace the rock particles, pushing them outwards perpendicular to the wave-path that leads to the earthquake-related first rolling period.
Surface waves (L-waves/ long waves)
- These waves move along the surface of the earth. They are responsible for the earthquake's carnage.
- They move up and down the Earth's surface, rocking the foundations of man-made structures.
- Surface waves are slowest of the three waves, which means that they are the last to arrive. So at the end of an earthquake usually comes the most powerful shaking.
Answer:
2) twice the amplitude and half the wavelength
Explanation:
