We make a graphic of this problem to define the angle.
The angle we can calculate through triangle relation, that is,
With this function we should only calculate the derivate in function of c
That is the rate of change of 
.
b) At this point we need only make a substitution of 0 for c in the equation previously found.
Hence we have finally the rate of change when c=0.
Answer:
a) From definition a transverse wave is which one where the elements moves perpendicular to the direction of the wave. For example is a wave is moving from the left to the right the elements would be wibrating or moving upward or downward.
We have a lot examples for a transverse wave. For example water waves, strings on the musical instruments , light and radio waves.
b) We can identify a transverse wave if the particles are displaced perpendicular to the direction of the wave. Usually these types of wave occur in elastic solids. And we can identify it when we see a pattern perpendicular between the wave direction and the particles motion. In simple words we need to see that the wave is moving down and up.
Explanation:
Part a
From definition a transverse wave is which one where the elements moves perpendicular to the direction of the wave. For example is a wave is moving from the left to the right the elements would be wibrating or moving upward or downward.
We have a lot examples for a transverse wave. For example water waves, strings on the musical instruments , light and radio waves.
Part b
We can identify a transverse wave if the particles are displaced perpendicular to the direction of the wave. Usually these types of wave occur in elastic solids. And we can identify it when we see a pattern perpendicular between the wave direction and the particles motion. In simple words we need to see that the wave is moving down and up.
The answer for this problem would be:
Assuming non-relativistic momentum, then you have:
ΔxΔp = mΔxΔv = h / (4)
Δv = h / (4πmΔx)
m ~ 1.67e-27 h ~ 6.62e-34,Δx = 4e-15 -->
Δv ~ 6.62e-34 / (4π * 1.67e-27 * 4e-15) ~ 7,886,270 m/s ~ 7.89e6 m/s
That's about 1% of the speed of light, the assumption that it's non-relativistic.
